
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?

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, ?

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

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

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,


Algebra Word Problems: 1. The length of the floor of a onestorey 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

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:

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

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

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

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

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

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

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

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.


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

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

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

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

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

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

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

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

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

Work the following area application problem. You are given the job of laying carpet for a sixstory 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


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:

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

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

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?

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

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

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

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

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

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


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

You are given the job of laying carpet for a sixstory 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

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 .

The volume of a cube is 125 cubic inches. Find the surface area. I know that the volume formula is V=Bh where v=volume, B=area of the base, and h=height. How do I get the surface area though? Also, The surface area of a cube is 384 square cm. Find the

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.(2x4)in^2 B.(8x8)in^2 C.(2x^24x)in^2 D.(4x^28x)in^2

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

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 facecentered cubic lattice, and show that it does not depend on the edge length of the unit cell ot on the size of

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 facecentered cubic lattice, and show that it does not depend on the edge length of the unit cell ot on the size of

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 .

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


I actually have two questions: 4. An open box is to be made from a rectangular piece of material 3m by 2m by cutting a congruent square from each corner and folding up the sides. What are the dimensions of the box of the largest volume made this way, and

How do I find the area and the volume of a prism using base10 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

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

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

Problem solving with derivatives. A rectangular box has square base of edge length x cm. Its framework of 12 edges is constructed from wire of total length 36cm. Find: i. the height of the box in terms of x ? ii. the volume of the box in terms of x? ii.

1. Chris makes an opentopped box from a 30cm by 30cm piece of cardboard by cutting out equal squares from the corners and folding up the flaps to make the sides. What are the dimensions of each square to the nearest hundredth of a centimetre, so that

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

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.

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.

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.


The volume of liquid flowing per second is called the volume flow rate "Q" and has the dimensions of [L]^3/[T]. The flow rate of a liquid through a hypodermic needle during an injection can be estimated with the following equation. Q = pi * R^n (P2  P1) /

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

Hi again, so when calculating a circle's dimensions, circumference and area do you use the squared symbol and for a rectangular prism's dimensions, surface area, and volume do you use the squared symbol? Please respond quickly!!! Thank You Very Much.

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?

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?

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

Bar BC in the figure has length L, constant cross sectional area A, and is composed of a homogeneous material with modulus E. The bar is fixed between walls at B (x=0) and C (x = L). The bar is subjected to a variable distributed load per unit length,

Bar BC in the figure has length L, constant cross sectional area A, and is composed of a homogeneous material with modulus E. The bar is fixed between walls at B (x=0) and C (x = L). The bar is subjected to a variable distributed load per unit length,

The volume enclosed by a sphere of radius r is (4/3)πr^3. The surface area of the same sphere is 4πr^2. You may already have noticed that the volume is exactly (1/3)r times the surface area. Explain why this relationship should be expected. One way is to

Using Cavalieri's Principle, determine which of these prisms does not have the same volume as the others? a. dimensions 10 cm, 6 cm, 4 cm, 8 cm b. dimensions 6 cm, 8 cm, 8 cm c. dimensions 4 cm, 8 cm, 12 cm d. dimensions 8 cm, 3 cm 9 cm I got for a. 1,920,


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

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?

A box with a square base and no top is to have a volume of 32 ft3. What dimensions use the least amount of material (in other words what dimensions give minimum outside surface area)?

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

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

Find the missing numbers for the dimensions and measures of a rectangular prism... Length 5 m Width ? Height ? Surface Area 94 m to the second power Volume 60 m to the third power Please answer the one's with a ?. Thank you.

have 50 sq ft of material to make an open top box with a square base. a) use formula for surface area to express the height h of the box in terms of x. b) find the dimensions of the box that will produce the maximum volume.

Im having severe trouble understanding the concept of Dimensions. And with 300 other students in my physics class the Professor doens't have alot of time for individual students.... The volume of a liquid flowing per second is called the volume flow rate Q

A farmer has 110 metres of fencing to fence off a rectangular area. Part of one side is a wall of length 15m. Find the dimensions of the ﬁeld that give the maximum area. Answers: length and width = 31,25m Thank you so much for a huge help.

You are going to build a glass box. The length of the box is 8 inches more than the width and the height is half the length. The length of the wire to make the frame is 108 inches. 1.What are the dimensions of the box? 2.All six faces of the box will be


PLEASE HELP ME WITH ALGEBRA II project!? Equipment: Tape Measure Purpose: The purpose of this lab is to practice multiplying, dividing, adding, and subtracting polynomials with a purpose in mind. I know this business trip will take valuable time, but it

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

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

1.A norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window find the dimensions of a Norman window of maximum area when the total permeter is 16ft. 2. A rectangle is bounded by the x axis and the semicircle

Please show all of your work in the space below. Please present and organized and complete solution. A garden will be made up of a parallelogram, a rectangle and a triangle. The garden must have an area of 500m square. Draw two possible gardens. Determine

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

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

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?

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

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.


A box with an open top has vertical sides, a square bottom, and a volume of 4 cubic meters. If the box has the least possible surface area, find its dimensions. Length of base= Height=

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?

The length script l, width w, and height h of a box change with time. At a certain instant the dimensions are script l = 7 m and w = h = 5 m, and script l and w are increasing at a rate of 6 m/s while h is decreasing at a rate of 4 m/s. At that instant

how would i work out the following problems solve each formula in terms of the given variable 1. 5d2g=9 ;g The formula A=2h(l+w) gives the lateral area a of a rectangular solids with length l, width,w and height h. 2. solve this formula for h 3. solve

An open box of maximum volume is to be made from a square piece of cardboard, 24 inches on each side, by cutting equal squares from the corners and turning up the sides to make the box. (a) Express the volume V of the box as a function of x, where x is

The given figure shows a rectangle inscribed in an isosceles right triangle whose hypotenuse is10 units long. Express theÃ¢â‚¬â€¹ ycoordinate of P in terms of x.Ã¢â‚¬â€¹ (Hint: Write an equation for the lineÃ¢â‚¬â€¹ AB.)

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

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 volume of a cone is 48 pi cubic units. If its dimensions are reduced to one half their original length, what would its new volume be?

Let R be the first quadrant region enclosed by the graph of y= 2e^x and the line x=k. a) Find the area of R in terms of k. b) Find the volume of the solid generated when R is rotated about the xaxis in terms of k. c) What is the volume in part (b) as k


The dimensions in inches of a shipping box can be expressed as width x, length x + 1, and height x  4. The volume is 84 ft^3. Find the dimensions of the box in feet. 1, 1, 4 2, 2, 21 2, 6, 7 3, 4, 7 Please help? If somebody can help put this into an

Applications of derivatives You are planning to make an open rectangular box from an 8 by 15 inch piece of cardboard by cutting congruent squares from the corners and folding up the sides. what are the dimensions of the box of largest volume you can make

a page of pictures for a yearbook is 8 1/2 inches by 11 inches. The space between the pictures is 3/16 inch. How high can each picture be to fit seven down the length of the page? since the the length of the page is 11 inches, and there has to be seven

use the formula v=lwh to find the volume of a rectangular prism with the following dimensions: • length = 7 in. • width = 4 in. • length = 3 in. a. v = 14 in.3 b. v = 31 in.3 c. v = 49 in.3 d. v = 84 in.3

1. A parking lot space is in 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? A.128ft2 B.266ft2 C276ft2**** D138ft2 2. Each blade on a windmill is in shape of a triangle with base of