# A box with no top is to be constructed from a piece of cardboard whose Width measures x inch and whose length measures 3 inch more than the width the box is to be formed by cutting squares that measure

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1. ## math

an open rectangular box is to be formed by cutting identical squares, each of side 2 in, one from each corner of a rectangular piece of cardboard, and then turning up the ends. If the area of the piece of cardboard is 160 inĀ² and the box is to have volume

2. ## Math

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 12 in by 12 in by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a

3. ## math

an open box is to be formed out of a rectangular piece of cardboard whose length is 8 cm longer than its width to form the box,a square of side 4 cm will be removed from each corner of the cardboard then the edges of the remaining cardboard will be turned

4. ## math

A box with a square base and no top is to be made from a square piece of cardboard by cutting 4-in. squares from each corner and folding up the sides, as shown in the figure. The box is to hold 324 in3. How big a piece of cardboard is needed?

5. ## Calculus

A cardboard box of 32in^3 volume with a square base and open top is to be constructed. What is the length of base that will minimize the surface area?

6. ## calculus

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 14 in. long and 6 in. wide, find the dimensions of the box that will yield the maximum

7. ## Calculus

Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 3 ft by 4 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this

8. ## math

A square piece of cardboard is to be used to form a box without a top by cutting off squares, 5cm on a side, from each corner and then folding up the sides. if the volume of the box must be 320 sq. sm, what must be the length of a side of the cardboard?

9. ## Pre Calculus

A piece of cardboard measuring 13 inches by 11 inches is formed into an open-top box by cutting squares with side length x from each corner and folding up the sides. a. Find a formula for the volume of the box in terms of x b. Find the value for x that

10. ## AP Calculus

A cardboard box of 108in cubed volume with a square base and no top constructed. Find the minimum area of the cardboard needed. (Optimization)

an open box with a volume of 1500cm cubed is to be constructed by taking a piece of cardboard of 20 cm by 40 cm, cutting squares of sides length x cm from each corner and folding up the sides. show that this can be done in two ways, and find exact

12. ## math

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions W inches by L inches by cutting out equal squares of side x at each corner and then folding up the sides. (W = 12 in. and L = 20 in). Find the values of x for

13. ## Math

A box with an open top is to be constructed by cutting a-inch squares from the corners of a rectangular sheet of tin whose length is twice its width. What size sheet will produce a box having a volume of 32 in^3, when a = 2? width in length in

14. ## Calculus

an open box is made by cutting out squares from the corners of a rectangular piece of cardboard and then turning up the sides. If the piece of cardboard is 12 cm by 24 cm, what are the dimensions of the box that has the largest volume made in this way?

15. ## Calculus 1

A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 18 in. by 30 in. by cutting out equal squares of side x at each corner and then folding up the sides as in the figure. Express the volume V of the box as a

16. ## Algebra 2

An open-top box is made from a 14-inch-by-32-inch piece of cardboard, as shown below. The volume of the box is represented by V(x) = x(14 - 2x)(32 - 2x), where x is the height of the box. a. Write the volume of the box as a polynomial function in standard

17. ## Math

A piece of cardboard measuring 11 inches by 12 inches is formed into an open-top box by cutting squares with side length x from each corner and folding up the sides. Find a formula for the volume of the box in terms of x V(x)= ? Find the value for x that

18. ## Algebra

A box with no top is to be constructed from a piece of cardboard whose length measures 6 inch more than its width. The box is to be formed by cutting squares that measure 2 inches on each side from the four corners an then folding up the sides. If the

19. ## math

A box with a square base and no top is to be made from a square piece of cardboard by cutting 4-in. squares from each corner and folding up the sides, as shown in the figure. The box is to hold 196 in3. How big a piece of cardboard is needed?

20. ## Math

a rectangular piece of cardboard is twice as long as it is wide . from each of its for corners, a square piece 3 inches on a side cut out. the flaps at each corner are then turned up to form an open box. if the volume of the box is 168 cubic inches, what

21. ## Calculus

A piece of cardboard measuring 13 inches by 14 inches is formed into an open-top box by cutting squares with side length x from each corner and folding up the sides. Find a formula for the volume of the box in terms of x V(x)= Find the value for x that

22. ## Algebra

A box with a square base and no top is to be made from a square piece of cardboard by cutting 4-in squares from each corner and folding up the sides... the box is told 100 in cube, how big a piece of cardboard is needed?

23. ## Maths - Algebra

Boxes are made by cutting 8cm squares from the corners of sheets of cardboard and then folding. The sheets of cardboard are 6cm lnbger than they are wide. width of sheet= x length of sheet = x+6 length of finished box = (x-10) width of finished box =

24. ## MATH help

A box with no top is to be constructed from a piece of cardboard whose Width measures x inch and whose length measures 3 inch more than the width the box is to be formed by cutting squares that measure 1 inch on each side of the 4 corners and then folding

25. ## pre-calc

A box with an open top is to be constructed by cutting equal-sized squares out of the corners of a 18 inch by 30 inch piece of cardboard and folding up the sides. a) Let w be the length of the sides of the cut out squares. Determine a function V that

26. ## Math- Math Analysis

In a rectangular piece of cardboard with a perimeter of 20ft, three parallel and equally spaces creases are made (so the piece is divided into four equal sections.) The cardboard is then folded to make a rectangular box with open square ends. a. Write a

27. ## Algebra

Identical squares are cut off from each corner of a rectangular piece of cardboard measuring 7cm by 12cm. The sides are then folded up to make a box with an open top. If the volume of the box is 33cm^3, what is the largest possible length of each side of

28. ## Calculus

Equal squares of side length x are removed from each corner of a 20 inch by 30 inch piece of cardboard, and the sides are turned up to form a box with no top. Write the volume V of the box as a function of x.

29. ## Calculus

A box (with no top) is to be constructed from a piece of cardboard of sides A and B by cutting out squares of length h from the corners and folding up the sides. Find the value of h that maximizes the volume of the box if A = 7 and B = 12

30. ## Engineering

A box with an open top is to be made from a square piece of cardboard by cutting equal squares from the corners and turning up the sides. If the piece of cardboard measures 12 in on the side, find the size of the squares that must be cut out to yield the

31. ## Basic Calculus

A piece of cardboard measuring 14 inches by 8 inches is formed into an open-top box by cutting squares with side length x from each corner and folding up the sides. FIND: 1). a formula for the volume of the box in terms of x 2). the value for x that will

32. ## Pre-Calc

An open box with a volume of 1500cm^3 is to be constructed by taking a piece of cardboard of 20 cm by 40 cm, cutting squares of sides length x cm from each corner and folding up the sides. Show that this can be done in two different ways, and find exact

33. ## math

a box is to be made by cutting out the corners of a square piece of cardboard and folding the edges up. if 3-inch squares are to be cut out of the corners and the box contains 243 cubic inches, what is the length of a side of the original cardboard square

34. ## Math

An open-topped box is constructed from a piece of cardboard with a length 2 cm longer than its width. A 6 cm square is cut from each corner and the flaps turned up from the sides of the box. If the volume of the box is 4050 cm3 , find the dimensions of the

35. ## math

a piece of cardboard is twice as it is wide. It is to be made into a box with an open top by cutting 2-in squares from each corner and folding up the sides. Let x represent the width (in inches) of the original piece of cardboard. a.Represent the length of

36. ## Math

A box with no top is to be constructed from a piece of cardboard whose Width measures x inch and whose length measures 3 inch more than the width the box is to be formed by cutting squares that measure 1 inch on each side of the 4 corners and then folding

37. ## Calculus

A box with an open top is to be made from a square piece of cardboard by cutting equal squares from the corners and turning up the sides. If the piece of cardboard measures 12 cm on the side, find the size of the squares that must be cut out to yield the

38. ## Mathematics

A box with an open top is been constructed from a piece of cardboard that is 4m wide by cutting a out a square from each side of that corner and bending up the side . Find the maximum volume

39. ## Calculus

Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 3 ft by 4 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this

40. ## Calculus

From each corner of a square piece of cardboard, remove a square of sides 3 inch. Turn up the edges to form an open box. If the box is to hold 300 inch cubed, what are the dimensions of the original piece of cardboard?

41. ## GRADE 12 APPLIED MATH

The Problem You are given a piece of cardboard that is 6 inches by 4 inches. You would like to cut equal-sized squares out of each of the 4 corners and fold the cardboard in such a way to make an open-top rectangular box. Part A: Complete the table below:

A pizza box top with a square base is to be made from a rectangular sheet of cardboard by cutting six 1-inch squares from the corners and the middle sections and folding up the sides. If the area of the base is to 144 in^2, what piece of cardboard should

43. ## College Math

An open-topped rectangular box is to be constructed from a 24 inch by 36 inch piece of cardboard by cutting out squares of equal sides from the corners and then folding up the sides. What size squares should be cut out of each of the corners in order to

44. ## Algebra 2

A rectangular piece of cardboard has length that is 16 inches more than the width. The area of the cardboard is 297 sq. in. Find the measures of its width and length. Enter width in., length in.

45. ## calc

by cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, the cardboard may be turned into an open box. if the cardboard is 16 inches long and 10 inches wide, find the dimensions of the box

46. ## Math

Suppose you take a piece of cardboard measuring 7 inches by 7 inches, cut out square corners with sides x inches long, and then fold up the cardboard to make an open box. Express the volume V of the box as a function of x.

47. ## math

A piece of cardboard measure 12ft by 12ft. Corners are to be cut from it as shown by the broken lines, and the sides folded up to make a box with an open top. What size corners should be cut from the cardboard to make a boxx with the greatest possible

48. ## math

A box with no top is to be constructed from a piece of cardboard whose width measures x cm and whose length measures 6 cm more than its width. The box is to be formed by cutting squares that measure 2 cm on each side from the four corners, and then folding

49. ## Algebra 2

A box with no top is to be constructed from a piece of cardboard whose length measures 12 inches more than its width. the box is formed by cutting squares that measures 4 inches on each sides from 4 corners and then folding up the sides. If the volume of

50. ## Math

A box with an open top is to be made by cutting 5-inch squares from the corners of a rectangular piece of cardboard whose length is twice its width and then folding up the remaining flaps. Let x represent the width of the original piece of cardboard;

51. ## Math

A piece of cardboard has a length of 60cm and a width of 40cm. In order to make the cardboard into an open box, a box with no lid), a piece of length x must be cut out of each corner. Write an equation to represent each dimension of the box.

52. ## pre calc

A box without a lid will be constructed from 75 cm x 100 cm piece of cardboard, by cutting squares of the same size from each corner, and folding up the sides. What is the approximate volume of the largest possible box that can be constructed?

53. ## Calculus

A box with an open top is to be constructed from a square piece of cardboard, 10in wide, by cutting out a square from each other of the four and bending up the sides. What is the maximum volume of such a box?

54. ## college algebra

A rectangular box with no top is to be constructed from a 10 in. x 10 in square piece of cardboard by cutting equal square of side x from each corner and then bending up the sides. Write the volume of the box as a function of x.

55. ## college algebra

A rectangular box with no top is to be constructed from a 10 in. x 10 in square piece of cardboard by cutting equal square of side x from each corner and then bending up the sides. Write the volume of the box as a function of x.

56. ## college algebra

A rectangular box with no top is to be constructed from a 10 in. x 10 in square piece of cardboard by cutting equal square of side x from each corner and then bending up the sides. Write the volume of the box as a function of x.

57. ## calculus

Help!!! A rectangle piece of cardboard twice as long as wide is to be made into an open box by cutting 2 in. squares from each corner and bending up the sides. (a) Express the volume V of the box as a function of the width W of the piece of cardboard (b)

58. ## Maths

A gift box is made from a rectangular piece of cardboard that is three times as long as it is wide. 5 cm squares are cut from each corner and the ends are then folded up to make the box. If the box's volume is 4340 cm^3, find the length and width of the

59. ## Pre-Calc

A box with a square base and no top is to be made from a square piece of cardboard by cutting 6 in. squares from each corner and folding up the sides. The box is to hold 11094 in cubed. How big a piece of cardboard is needed? ___in. by ___ in.

60. ## math

Reza is helping En Shah to make a box without the top.The box is made by cutting away four squares from the corners of a 30cm square piece of cardboard as shown in Figure 1 and bending up the resulting cardboard to form the walls of the box.

61. ## math

The length of a rectangular piece of cardboard is three more than twice the width. A square 2 cm on a side is cut out of each corner. The sides are folded up to form an open box. if the volume of the box is 120cm^3, what were the original dimensions of the

62. ## algebra

A rectangular piece of cardboard is 2 units longer than it is wide? From each of its corner a square piece 2 units on a side is cut out.The flaps are then turned up to form an open box that has a volume of 70 cubic units.Find the length and width of the

63. ## algebra 2

you can make an open box from a piece of flat cardboard. First cut congruent squares from the four corners of the cardboard. Then fold and tape the sides. let x equal the side of each congruent squares as x increases so does the depth of the box the

64. ## calculus

A closed cardboard box is made with a square top and bottom, and a square horizontal shelf inside that divides the interior in half. A total of 12 square meters of cardboard is used to make the top, sides, bottom, and shelf of the box. What should the

65. ## College Algebra

a box with an open top is constructed from a rectangular piece of cardboard with dimensions 14 inches by 18 inches by cutting out and discarding equal squares of side x at each corner and then folding up the sides as in the figure. The cost to create such

66. ## algebra

Volume of a Box A box is constructed by cutting out square corners of a rectangular piece of cardboard and folding up the sides. If the cutout corners have sides with length x, then the volume of the box is given by the polynomial A box is constructed from

67. ## Calculus

An open box is to be made from cutting squares of side "s" from each corner of a piece of cardboard 25" by 30". Write an expression for the volume, V, of the box in terms of s. -I have no idea where to start on this. I know V=lwh (length*width*height), but

68. ## Math

An open box is to be made from a 11 inch by 11 inch piece of cardboad. this box is constructed by cutting squares that measure x inches on each side from the corners of the cardboard and turning up the sides. Use a graphical calculator to find the height

69. ## Calculus

Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 37ft by 20 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that can be formed in this

70. ## Pre cal

A box with a square base and no top is to be made from a square piece of carboard by cutting 8 in. squares from each corner and folding up the sides. The box is to hold 7200 in. How big a piece of cardboard is needed?

71. ## Math, Pre-calculas

From each corner of a square piece of cardboard, a square with sides of 3cm is removed. The edges are then up to form an open box. If the box is to hold 243cm^3, what are the dimensions of the original piece of cardboard?

72. ## pre calculus

A box with a square base and no top is to be made from a square piece of carboard by cutting 5 in. squares from each corner and folding up the sides. The box is to hold 23805 in3. How big a piece of cardboard is needed?

73. ## calculus

A box with a square base and no top is to be made from a square piece of carboard by cutting 7 in. squares from each corner and folding up the sides. The box is to hold 16128 in3. How big a piece of cardboard is needed? ?in by ?in

74. ## calculus

A box with a square base and no top is to be made from a square piece of carboard by cutting 3 in. squares from each corner and folding up the sides. The box is to hold 7500 in3. How big a piece of cardboard is needed? ?in by ?in

75. ## Math

Square with sides of length are cut out of each corner of a rectangle Mylar piece of cardboard measuring 13ft by 8ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the box. B. Supposed that in part a the

76. ## Pre-Cal

A box with a square base and an open top is constructed from 5400 cm^2 of cardboard. Find the dimensions of the largest possible box. I know the answer is : base lenght - 42.4 cm height- 21.2 cm please help me, thank you so much :)

77. ## Algebra

A rectangular piece of cardboard is 15 inches longer than it is wide. If 5 inches are cut from each corner, and the remaining fold up to form a box,the volume of the box is 1250 cubic inches. Find the dimensions of the piece of cardboard.

78. ## AFM (MATH)

a) Write an equation to represent the volume of an open box constructed by cutting congruent squares from the corners of a 24" by 14" piece of cardboard. b) What is the domain of this model?

79. ## chemistry

A box with a square base and no top is to be made from a square piece of carboard by cutting 7 in. squares from each corner and folding up the sides. The box is to hold 16128 in3. How big a piece of cardboard is needed? Your answer is ?in by ?in Ooops, I

80. ## Pre-calc

A cardboard box with an open top and a square bottom is to have a volume of 45 ft3 . Use a table utility to determine the dimensions of the box to the nearest 0.1 foot that will minimize the amount of cardboard used to construct the box.

81. ## math

from a square piece of cardboard with length and width of x inches, a square of width x-1 inches is removed from the center. Write the area of the remaining piece of cardboard as a function of x

82. ## algebra

An open topped box is constructed from a 20 inch by 15 inch piece of cardboard by cutting equally sized squares from each corner and folding up the resulting flaps. What is the maximum volume of the box? Be sure your answer is to this prompt! Round your

83. ## Calculus

A box with a square-base is to be constructed with no top. The bottom face will cost 4 times as much as the sides. The volume of the box will be 0.5 m3. What dimensions (length, width and height) will minimize the cost to construct this box?

84. ## math 12

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85. ## Math

The length of a piece of cardboard is two inches more than its width. an open box is formed by cutting out 4 inch squares from each corner and folding the sides. If the volume of the box is 672 cubic inches, find the dimensions.

86. ## Calculus

A rectangular box opens Ata the top is to be formed from a rectangular piece of cardboard which is 3 m * 8m. What size of square should be cut from each corner to form the box with maximum volume.?

87. ## math

You cut square corners from a piece of cardboard that has dimensions 32 cm by 40 cm. You then fold the cardboard to create a box with no lid. To the nearest centimeter, what are the dimensions of the box that will have the greatest volume?

88. ## maths

a box is to be made from the piece of cardboard at right, where square corners of side x are to be cut out, and sides folded up, and top enclosed. Find the possible heights x of the sides when the volume of the box is 10, within the interval of length 1

89. ## algebra

An open-top box is to be constructed from a 6 foot by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. 1. Find the function V that

90. ## math

a tray with a square base is to be made from a square piece of cardboard by cutting 5 inch squares from each corner and folding up the sides. If the box is to hold a volume 520 cubic inches, find the length of the piece of cardboard that is needed.

91. ## Math

a tray with a square base is to be made from a square piece of cardboard by cutting 5 inch squares from each corner and folding up the sides. If the box is to hold a volume 520 cubic inches, find the length of the piece of cardboard that is needed.

92. ## calculus optimization problem

by cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. if the cardboard is 30 inches long and 14 inches wide find the dimensions of the box that will yield the

93. ## calc

an open box is to be made from a 4 ft by 5 ft piece of cardboard by cutting out squares of equals sizes with width x ft from the four corners and bending up the flaps to form sides.express the volume of the open box as a function of x what is the domain of

94. ## math

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 16 in. long and 6 in. wide, find the dimensions of the box that will yield the maximum

95. ## Calculus

By cutting away identical squares from each corner of a rectangular piece of cardboard and folding up the resulting flaps, an open box may be made. If the cardboard is 16 in. long and 10 in. wide, find the dimensions of the box that will yield the maximum

96. ## Math

A function that represents the volume of a cardboard box is V(x) = -0.65x^3 + 4x^2 + 3x, where x is the width of the box. Determine the width that will maximize the volume. What are the restrictions on the width? The answer is 4.45 and domain is 0

97. ## Math

Suppose you take a piece of cardboard measuring 7 inches by 7 inches, cut out square corners with sides x inches long, and then fold up the cardboard to make an open box. Express the volume V of the box as a function of x.

98. ## math

An open-top box is to be constructed from a 6 foot by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a)

99. ## algebra

An open-top box is to be constructed from a 6 foot by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. a)

100. ## Math

Please help I have no Idea what to do here. A box with an open top is to be constructed by cutting a-inch squares from the corners of a rectangular sheet of tin whose length is twice its width. What size sheet will produce a box having a volume of 420 in^3