# How are length, area, and volume related in terms of the three dimensions of space?

77,020 results

1. ### area/length/volume

How are length, area, and volume related in terms of the three dimensions of space? and How is it possible for objects of the same volume to have different masses?
2. ### area/length/volume

How are length, area, and volume related in terms of the three dimensions of space? and How is it possible for objects of the same volume to have different masses? #2 Gads! Think of a cup full of steel marbles and a cup full of cotton balls. ummm, ?
3. ### math

The area of a rectangular space is 128 square feet. a. Find all the possible pairs of whole number dimensions in feet. b. Explain which pair allows enough space for a car to park. c. If the length of the space is x feet, how would you describ e the width using the area and the...
4. ### Algebra

Volume and surface area are often compared by manufacturers in order to maximize how much of something can go inside of a package (volume) while keeping how much material is required to create the package (surface area) low. Pick a product that might be packaged in the shape ...
5. ### College Algebra

The campus of a college has plans to construct a rectangular parking lot on land bordered on one side by a highway. There are 720 feet of fencing available to fence the other three sides. Let x represent the length of each of the two parallel sides of fencing. a) Express the ...
6. ### Algebra

A community college campus plans to construct a rectangular parking lot on land bordered on one side by a highway. There are 640 feet of fencing available to fend the other three sides. Let x represent the length of each of the two parallel sides of fencing. a) Express the ...
7. ### Calculus

A construction company wants to build a rectangular enclosure with an area of 1000 square feet by fencing in three sides and using its office building as the fourth side. Your objective as supervising engineer is to design the enclosure so that it uses the least amount of ...
8. ### Applied Math- Gr.11

A farmer wants to enclose three sides of a rectangular pasture unsing 1000 yards of fencing. The fourth side does not require fencing because it borders a river. What dimensions (length and width) should the farmer choose in order to enclose the greatest area? a) Find at least...
9. ### pre-calc

area of a rectangular region: a farmer wishes to create two rectangular regions bordering a river, by three fences perpendicular to the river and one connecting them. suppose that x represents the length of each of the three parallel pieces of fencing. she has 600 feet of ...
10. ### Algebra

Algebra Word Problems: 1. The length of the floor of a one-storey building is 14 feet longer than its width. The building has 1,632 square feet of floor space. Write a quadratic equation for the area of the floor in terms of w. Find the length and width of the floor. 2. A ...
11. ### Geometry

A rectangular prism has a base that is 5 cm by 7 cm and a height of 12 cm. If all dimensions are doubled, what happens to the volume? A. When the dimensions are doubled, the volume is twice the original volume. B. When the dimensions are doubled, the volume is three times the ...
12. ### Math

A production crew is assembling a three-level platform inside a stadium for a performance. The platform has the dimensions of 4x long and 2x wide, the middle box has the dimensions of 6x long and 4x wide, and the bottom box has the dimensions of 8x long and 6x wide. What is ...
13. ### algebra

a production crew is assembling a three-level platform inside a stadium for a performance. the platform has dimensions shown in the diagram and has a total volume of 1250 cubic feet. What is the volume, in terms of x, for each of the three levels of the platform?
14. ### Pre Calc

Given the sum of all the edges of the rectangular solid at the right is 76cm, the area of all of its faces is 228 cm^2, and its volume is 216 cm^3. Find its height, width and length. [hint- Let the height, width and length be the roots of a cubic polynomial x^3 + ax^2 + bx +c=...
15. ### Math

We want to construct a closed rectangular box whose base has a length three times the width. The surface area has to be 600 cm2. Determine the dimensions of the box that will produce the largest volume.
16. ### Calculus

A festivals being planned. The planners need to enclose to adjacent 200 M^2 areas with fencing. They have budgeted \$1000 for fencing. Fencing currently cost \$10/meter. The diagram of the area is as follows: 1. Write an equation representing the total length of fence, L, needed...
17. ### Caclulus

Let x and y be to positive numbers whose product is 500: (a) Find the maximum sum of x and y (b) Find the minimum sum of x and y: 2. A cylindrical container can hold a volume of 1 liter. Find the dimensions of the container that minimizes the surface area. 3. What are the ...
18. ### Math

Dylan plants grass in a rectangle space behind the clump house.nthe area of the space was 70 ft. If the length of the space is 14 ft. What's the width of the space
19. ### algebra

I need someone to check my work not sure if I'm doing this right. The design of a digital box camera maximizes the volume while keeping the sum of the dimensions at 6 inches. If the length must be 1.5 times the height, what should each dimension be? HINT: Let x represent one ...
20. ### Pre-Calculus

Tommy is building a rectangular playpen for his pigs where one side of the play area is a side of his barn. He has enough material to make a fence with a total length of 160 feet. write a función that represents the playpen's área in terms of its length perpendicular to the ...
21. ### mat117/algebra

If the sides of a square are increased by 3 cm, the area is decreased by 36 cm^2. What were the dimensions of the original square? Please show me the formula and how to work. That doesn't sound possible. If the sides of a square are increased, the area must also be increased. ...
22. ### Math

Find the Maximum area for the given perimeter of a rectangle. State the length and width of the rectangle. 28 inches Well, finally a calculus problem. Ok, we know that the area for a rectangle is A=l*w and the perimeter is P=2(l+w) In this problem P= 28, so let's express one ...
23. ### Pre-Calc

One campus of HCC has plans to construct rectangular parking lot on land bordered on one side by a highway. There are 640 ft of fencing available to fence the other sides. Let x represent the length of each of the two parallel sides of fencing. a. draw the illustration of the ...
24. ### Math

A box manufacturer wants to produce an open box for which the volume is 2 cubic meters and the length is twice the width. What actual dimensions of he box will require the least amount of material? Work: V = 2m^3 2m^3 = (w)*(2w)*(h) Possible dimensions: length width height ...
25. ### Math

Optimization Problem A right circular cylindrical can of volume 128tπ cm^3 is to be manufactured by a company to store their newest kind of soup. They want to minimize the surface area of the can to keep costs down. What are the dimensions of the can with minimum surface ...
26. ### pre- calc

area of a parking lot: One campus of Houston community college has plans to construct a rectangular parking lot on land bordered on one side by a highway. there are 640 feet of fencing available to fence the sides. let x represent the length of each off the two parallel sides ...
27. ### algebra

Ian wants to build a rectangular pen for his animals. One side of the pen will be against the barn; the other three sides will be enclosed with wire fencing. If Ian has 450 feet of fencing, what dimensions would maximize the area of the pen? a) Let w be the length of the pen ...
28. ### volume:ration

A worm has a diameter of 2.4cm and its length is upto 1.9M. a)How do I calculate the surface area? b)How do I calculate the volume? c)How do I work out the volume ratio of the worm? Please help! Thanx kim xxx Surface area= PI*2*radius * length] Volume= PI * radius^2 * length ...
29. ### math

a rectangle is twice as long as it is wide. if both of its dimensions are increased by 4m, its area is increased by 88m^2 find the dimensions of the original rectangle Original rectangle = w for width and 2w for length. Area = w x 2w Larger rectangle = w+4 for width and 2w+4 ...
30. ### Math

A postal service says that a rectangular package can have a maximum combined length and girth of 108 inches. The girth of a package is the distance around the perimeter of a face that does not include the length. a. Identify an inequality that represents the allowable ...
31. ### Algebra

1. The area of a rectangle is 12 and the width is 3/4 the length. What are the dimensions? 2. One leg of a right triangle is 2 1/2 times the other and the area is 20. What are the dimensions?
32. ### Calculus

A festivals being planned. The planners need to enclose to adjacent 200 M^2 areas with fencing. They have budgeted \$1000 for fencing. Fencing currently cost \$10/meter. The diagram of the area is as follows: (The diagram is 2 adjacent squares, the areas of both squares are 200 ...
33. ### math

Work the following area application problem. You are given the job of laying carpet for a six-story building. At each floor the dimensions of the floor are 75 meters in length by 40 meters in width. A stairwell takes up a space 2.5 m by 1.5 m, and cuts through each floor. If ...
34. ### math

What si the volume and surface area of a triangular prism with the dimensions of a 2.5 base, 2.5 height, and 7 length
35. ### math

Three rectangles have exactly the same area. The dimensions of each rectangle (as length and width) are a and b; a – 3 and b + 2; and a + 3 and b – 1. Find the area of the rectangles.
36. ### math

Three rectangles have exactly the same area. The dimensions of each rectangle (as length and width) are a and b; a – 3 and b + 2; and a + 3 and b – 1. Find the area of the rectangles.
37. ### math

Three rectangles have exactly the same area. The dimensions of each rectangle (as length and width) are a and b; a – 3 and b + 2; and a + 3 and b – 1. Find the area of the rectangles.
38. ### Math

Three rectangles have exactly the same area. The dimensions of each rectangle (as length and width) are a and b; a – 3 and b + 2; and a + 3 and b – 1. Find the area of the rectangles.
39. ### Algebra 2

A square has a length of x inches and a width of 2 inches less than the length. If the dimensions were doubled, what would be the area of the new square in terms of x? A.(2x-4)in^2 B.(8x-8)in^2 C.(2x^2-4x)in^2 D.(4x^2-8x)in^2
40. ### Math - Calculus

Im trying to understand related rates here and im getting stuck at this word problem. It says if V is the volume of a sphere with radius r, and the volume of the sphere decreases as the time passes. express dV/dt in terms of dr/dt. Describe the relationship in words. I don't ...

1. If a ping pong ball falls from the top of a building that is 168 feet high, how many seconds will it take the ball to hit the ground? Remember, the formula for distance is d = 16t^2. (1 point) 1 3.2 10.5 16 2. The volume of a box can be found by multiplying the length times...
42. ### Pre Calculus

1. A rectangular box has a square base, four sides, but no top. It has a volume of 20 cubic feet. Let A be the surface area of the box, and L the length of one side of the base. (a) The volume is measured in cubic feet. What units are convenient to use for the area A and the ...
43. ### Math

Manuel wants to build a rectangular pen for his animals. One side of the pen will be against the barn; the other three sides will be enclosed with wire fencing. If Manuel has 750 feet of fencing, what dimensions would maximize the area of the pen? a) Let w be the length of the...
44. ### Calculus, Math word problems.

A closed box is to be made in the shape of a cubiod, of height h cm and with a square base that has sides of length x cm. Its volume V is required to be 500 cm^3. A) write an expression for the V (volume)in terms of h and x. B)Write an expression for the surface area A in ...
45. ### science

For this activity, we had to make cube shaped models to represent cells. Then we had to compare aurafve area, volume, and surface area to volume ratio (SA:V) between the cells. Cell A: length of one side=1cm Surface area= 6cm^2 Volume= 1cm^3 SA:V= 6 Cell B: Length of one side...
46. ### science

You measure the dimensions of a rectangular block of aluminum to determine its volume. It has the following dimensions. length = 10.27 cm; width = 4.92 cm; height = 1.53 cm Assuming that each of these measurements is accurate to the nearest 0.01 cm, find the volume of the ...
47. ### Science

For this activity, we had to make cube shaped models to represent cells. Then we had to compare surface area, volume, and surface area to volume ratio (SA:V) between the cells.  Cell A:  length of one side=1cm  Surface area= 6cm^2  Volume= 1cm^3  SA:V= 6  Cell B:  ...
48. ### Calculus

A rancher wants to build a rectangular pen with an area of 150 m2. Let W be the width of the pen and L be the length of the pen. a. Find an equation for the perimeter P in terms of W and L . b. Use the given area to write an equation that relates W and L . c. Find the pen ...
49. ### Math

Andie is designing a rectangular play space for her dogs. The length of the play space is 7ft. and the width is 6ft. The new space will have a length and width twice the dimensions of the current space. She needs to purchase sod to cover the ground inside the play space. Write...

For this assignment, you are to create a Policy Manual for new managers. This manual should provide guidance to the new incoming managers, as they set up their respective departments. This manual should clearly lay out the expectations that you, as the owner and CEO of this ...
51. ### Math

You are given the job of laying carpet for a six-story building. At each floor the dimensions of the floor are 75 meters in length by 40 meters in width. A stairwell takes up a space 2.5 m by 1.5 m, and cuts through each floor. If the rest of the floor area is to be carpeted, ...
52. ### Math

Area is calculated in _______ dimensions, and volume is calculated in ___________? a. two, two b. two, three c. three, two d. three, three I think the answer is B
53. ### Algebra II

Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters is given by V(s) _ s3 _ 13s2 _ 54s _ 72. a) Find V(10). b) If the new width is s _ 6 centimeters, then what are the new ...
54. ### Math: Pre-calculus

A rancher wants to build a rectangular pen with an area of 180 . Let W be the width of the pen and L be the length of the pen. a) Find an equation for the perimeter P in terms of W and L . b) Use the given area to write an equation that relates W and L . c) Find the pen ...
55. ### Bus Management & Leadership

You are the owner and CEO of a brand new Internet access company, known as the XYZ Internet Company. For this assignment, you are to create a Policy Manual for new managers. This manual should provide guidance to the new incoming managers, as they set up their respective ...
56. ### calculus

Your task is to design a rectangular industrial warehouse consisting of three separate spaces of equal size.? The wall materials cost \$58 per linear foot and your company has allocated \$27840 for those walls. 1) The dimensions which use all of the budget and maximize total ...

mrs. watterson wants to fence in an area for her dog. she has 72 feet of fencing and wants to use all of it to enclose a space with the greatest possible area. which dimensions will give her a space with the greatest possible area? (1 point) 16 feet by 20 feet 18 feet by 18 ...
58. ### maths

According to health and safety policy, classrooms should allow for 1.8sqm of floor space per person and an additional 9sqm. A plan indicates that a classroom's floor dimensions should be 12.0m by 4.5m a Based on these figures, clculate the maximum number of students that can ...
59. ### chemistry help!

Hello, I am having problem with two lab questions and was wondering if someone can help! 1. Calculate the percentage of the empty space in a face-centered cubic lattice, and show that it does not depend on the edge length of the unit cell ot on the size of the atoms in the ...
60. ### chemistry

Hello, I am having problem with two lab questions and was wondering if someone can help! 1. Calculate the percentage of the empty space in a face-centered cubic lattice, and show that it does not depend on the edge length of the unit cell ot on the size of the atoms in the ...
61. ### Algebra

Suppose you want to enclose a rectangular garden plot against a house using fencing on three sides, as shown at the left. Assume you have 50 ft. of fencing material and want to create a garden with an area of 150 ft². A. Let w = the width. Write an expression for the length ...
62. ### Math 3 grd

How do I find the area and the volume of a prism using base-10 blocks? well, the area is found by multiplying length x width. so it would be 10 x 10, which equals 100. The volume, however, isn't much more work to find the answer. Volume=length x width x height... which means ...
63. ### Geometry

A rectangular prism has the following characteristics. It has a volume of 71 cubic inches. The sum of the three lengths is 14. The width is 2 less than the length. The length is 5 more than the height. What are the dimensions of this rectangular prism? Need help on finding ...

A pentagonal prism has dimensions that are four times the dimensions of a similar pentagonal prism. So its volume is _____times the volume of the smaller prism. A) 64 B) 8 C)16 D)4 Would it be A) 64? Next Question: If the dimensions of a cylinder are doubled the surface area ...
65. ### Calculus

A rancher wants to build a rectangular pen with an area of 150 m^2? a. Find an equation for the perimeter P in terms of W and L . b. Use the given area to write an equation that relates W and L . c. Find the pen dimensions that require the minimum amount of fencing. Width = ...
66. ### algebra

Decreasing cube. Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters is given by V(s) = s3 - 13s2 + 54s -72. a) Find V(10). b) If the new width is s - 6 centimeters, then ...
67. ### math

The length of a rectangular solid is three times the width. Find the volume and the length of its diagonal if the total surface area is 198 square inch
68. ### Math

A right rectangular prism is packed with identical cubes. The dimensions of the prism are given in terms of the number of cubes needed to fill the prism. length is 16 cubes wide th is 9 cubes height is 23 cubes. The side length of each cube is 1/4 inch. What us the volume?
69. ### math

Mr. Harrison has a very large backyard. He contacted the Clover Pool Company to have a pool installed in the shape of a rectangle. The Clover Pool Company would build a pool that has a perimeter of 72 yards. Mr. Harrison would be allowed to choose the dimensions (length and ...
70. ### math

A rectangular prism has a volume of 8 cubic yards. Assume the dimensions are whole numbers. What dimensions yield a prism with the greatest surface area? the leaset surface area?
71. ### Math

Postal regulations specify that a package sent by priority mail may have a combined length and girth of no more than 129 in. Find the dimensions of a cylindrical package with the greatest volume that may be sent by priority mail. Hint: The length plus the girth is 2πr + l...

A wire of length 380 cm is cut into 10 pieces.Each piece is then bent to form a square.The dimensions of the first three smallest squares are shown below.Find the value of x and hence,the area of the eighth largest square. x cm[ ] (x+1)cm [ ] x cm (x+1)cm (x+2)cm[ ] (x+2)cm ...
73. ### math

Find the dimensions of an open topped box that can be made from 3600 cm^2 of cardboard, if the length of the base is three times as long as its width. What is the maximum volume?
74. ### MATHS HELP plz

A parcel in the form of a rectangular block is held together by three pieces of tape . The parcel has square ends of side x cm and is y cm in length. Express the total length of tape in terms of x and y. Given tat the total length of tape is 450 cm, express the volume, V cm3 (...
75. ### Math

1. The length of a rectangle is 6 inches longer than thrice its width. The area of the rectangle is 57 square inches. Write a quadratic equation for the area of the floor in terms of x. Find the length and width of the rectangle. 2. If 1,500 ft of fencing is available to build...
76. ### Algebra 2

a computer manufacturer needs to change the dimensions of its foam packaging for a new model of computer. the width of the original piece is three times the height, and he length is equal to the height squared. The volume of the new piece can be represented by the equation V(h...
77. ### Algerbra

The area of a rectangle is 243cm^2. The length is three times greater than the width. What are the dimensions of the rectangle?
78. ### Calculus

A rectangular piece of tin has an area of 1334 square inches. A square tab of 3 inches is cut from each corner, and the ends and sides are turned up to make an open box. If the volume of the box is 2760 cubic inches, what were the original dimensions of the rectangular piece ...
79. ### MATHS HELP plz!!

A parcel in the form of a rectangular block is held together by three pieces of tape as shown in the diagram . The parcel has square ends of side x cm and is y cm in length. Express the total length of tape in terms of x and y. Given tat the total length of tape is 450 cm, ...
80. ### MATH QUIZ PLS HELP!!!

1.Find the lateral area of a cone with a radius of 7 ft. and a slant height of 13 ft. Use 3.14 for ©£ and round to the nearest tenth. 439.6 ft^2 324.5 ft^2 571.5 ft^2 285.7 ft^2*** 2.Find the surface area of a square pyramid with a base length of 24 cm and a height of 16 cm...
81. ### algebra

The length of a rectangle is 1 inch greater than its width. If the dimensions are doubled, its area increases by 36 square inched. Which equation could be used to find its dimensions?
82. ### Algebra

the length of a rectangle is 1 inch greater than its width if its dimensions are doubled its area increases by 36 square inches give an equation to find its dimensions
83. ### earth science

which term is best defined as a measure of the amount of space a subtance occupies? volume It looks like you have answered your own question. If it is three dimensional, it is volume. However, if it is two dimensional, it is area. I hope this helps a little more. Thanks for ...
84. ### math

a box has a surface area of 184 sq in give the dimensions it could have for its length width and height hint find three areas that add up to 92 square inches
85. ### Geometry

Find the missing numbers for the dimensions and measures of a rectangular prism... Length ? Width 7 m Height 5 m Surface Area 214 m to the second power Volume ? Please answer the one's with a ?. Thank you.
86. ### Geometry

Find the missing numbers for the dimensions and measures of a rectangular prism... Length ? Width 2.5 m Height 4.6 m Surface Area ? Volume 172.5 m to the third power Please answer the one's with a ?. Thank you.
87. ### math

If the length of football field is 40 yards ;ass than three times the width. the total area 6400 sq, yards what are the dimensions.
88. ### alegabra

a company making rectangular fish tanks is restricting the sum of their total dimensions to 52 inches.for one group of designs.the length and width will be the same.which of the following functions represents the volume in terms of the width?
89. ### math

the volume of a rectangular prism is 2,058 cm3. The length of the prism is three times the width. The height is 14 centimeters. Find the other dimensions
90. ### Algebra

Decreasing cube. Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters is given by V(s) equals s power of 3 - 13s power of 2 + 54s - 72. a) Find V(10). b) If the new width...
91. ### math

The length of a rectangle is 2 inches longer than the width. The area of the rectangle is 56 in^2. Find the dimensions. Also: The length of a rectangle is 3 ft more than the width. The area of the rectangle is 28 ft^2. Find the dimensions.
92. ### math

a rectangle has an area of 4(x+3)square units. if the dimensions are doubled what is the area of the new rectangle terms of x.will the ratio of the area of the original rectangle to the area of the larger rectangle be the same for any positive value of x?
93. ### Math

A rectangular prism has a volume of 960cm. It's width, length, and height are in the ratio 3:5:8. A) Determine the dimensions of the prism B) What is the ratio of the left side to the front to the top of the prism by surface area? C) Calculate the surface area of the prism.
94. ### Physics

As you know, a cube with each side 4 m in length has a volume of 64 m3. Each side of the cube is now doubled in length. What is the ratio of the new volume to the old volume? Why is this ratio not simply 2? Include a sketch with dimensions.
95. ### Optimization Calculus

A three sided fence is to be built next to a straight section of river, which forms the fourth side of a rectangular region. There is 96 ft of fencing available. Find the maximum enclosed area and the dimensions of the corresponding enclosure. I drew a picture of it and I got ...
96. ### Problems in three dimensions

A regular tetrahedron has sides of length s. Show that the surface area, A, of the tetrahedron can be determined using the formula A= square root of 3s^2
97. ### math

A parking lot space is in the shape of a rectangle. If the space has a length of 23 feet and a width of 12 feet, what is the area of the parking space?
98. ### Maths

The area of a rectangle of width ycm is 140cm^2. If the width is reduced by 2cm, the length increases by 3cm, and the area decreases to 136cm^2 to form an equation that enables you to determine the value of Y and hence, find the diagonal of the original rectangle workings. ...
99. ### Calculus - Optimization

A parcel delivery service a package only of the length plus girth (distance around) does not exceed 24 inches. A) Find the dimensions of a rectangular box with square ends that satisfies the delivery service's restriction and has a maximum volume. What is the maximum volume? B...
100. ### Math help, anyone?

Find the volume of a square pyramid with a base length of 9 cm and a height of 4 cm. 324 cm3 108 cm3 36 cm3 152 cm3 Find the volume of a cone with a radius of 10 mm and a height of 6 mm. 628 mm3 600 mm3 1,884 mm3 1,254 mm3 Find the lateral area of a cone with a radius of 7 ft...