Question

an open topped box is created by taking a 10 inch by 16 inch sheet of cardboard ans cutting out squares or length x from each corner and folding up the sides. what length would create a box of 64 cubic in?

Answer 1

x = 4 in

Explanation:

Volume of the open box is:

V(b) = 64 in³

And is equal to:

V(b) = L * w * h length * wide * heigh

According to the problem statement

x the side of the squares to be cut must be x ≤ 5

since 5 inches for x means no box at all

On the other hand, if we get factors for 64

64 = 2*2*2*2*2*2 or 64 = 8 * 4 * 2

Then values for x could be 4 and 2, evaluating x = 4

Then L = 16 one side of the box is 16 - 2*x = 8 in

The other w = 10 10 - 2*x = 2 in

And The volume is: V(b) = 8*2*4 = 64 in³

Answer 2

4 inches

Explanation:

Since the cardboard is being cut into square pieces this means that the 3D box is also going to be square. That also means that every single side will have the same length. Therefore, to calculate the length that would create a 64 cubic in box we simply find the cubic square root of 64... simply plug this into the calculator and you get the following...

`\sqrt[3]{64}` = 4 inches.