Question

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 2527 in3. How big a piece of cardboard is needed?

Answer 1

To find the size of the cardboard needed to make the box, we need to determine the dimensions of the square base and solve an equation for volume. The size of the cardboard needed is approximately 38.14 inches.

Step-by-step explanation:

To determine the size of the cardboard needed to make the box, we need to find the dimensions of the square base. Let's assume the side length of the square base is x inches. When we cut 7-inch squares from each corner and fold up the sides, the new height of the box will also be 7 inches. The volume of the box is given as 2527 cubic inches.

The volume of a rectangular prism is calculated by multiplying the length, width, and height. In this case, the length and width of the base are both x inches, and the height is 7 inches. So, the volume equation becomes x * x * 7 = 2527.

Solving the equation, we find x^2 = 363, which means x = sqrt(363) ≈ 19.07 inches. Since the dimensions of the larger square are twice that of the smaller square, the size of the cardboard needed would be 2 * 19.07 = 38.14 inches.

Answer 2

The size of the cardboard should be
`26 in\ by\ 26in`

Step-by-step explanation:

The diagram for this question is shown on the first uploaded image

The volume of the box is
`V = 2527 \ in ^3`

The length and the Width of the card is

L = W = Z

From the question we are told that 7 in squares were cut from each corner

So the length and the width of the box would be

L = W = (Z - 7)

And the height would be H = 7 in

Mathematically the volume of the box can be represented as

`V = Length\ of\ bx * Width\ of\ box * Height\ of\ box`

So the Volume would be

`V = (Z-7)(Z-7) * 7`

Substituting values

`(Z-7) ^2 = (2527)/(7)`

`(Z-7) ^2 = 361`

`(Z-7) ^2 = 19^2`

=>
`Z - 7 = 19`

`Z = 19 + 7`

`Z =26 \ in`