Question

What is the volume of the largest box that can be made from a square piece of cardboard with side lengths of 24 inches by cutting equal squares from each corner and turning up the sides?

Answer 1

Answer:

64 inches^3

Step-by-step explanation:

Since it’s asking for equal squares, you would have to have six equivalent pieces, which would form a cube. The largest factor of 24 with one being 6 would have to be 4. Now you have the 6 sides of your cube. Each side has an edge that equals 4 inches. Taking the formula for volume(l•w•h), you get 4x4x4. 4x4=16 and 16x4=64! In the end, the volume would be 64 in^3

Answer 2

Answer:

1024 in³

Step-by-step explanation:

Volume = (24 - 2x)(24 - 2x)(x)

= 576x - 96x² + 4x³

dV/dx = 576 - 192x + 12x² = 0

x² - 16x + 48 = 0

x² - 12x - 4x + 48 = 0

x(x - 12) - 4(x - 12) = 0

(x - 12)(x - 4) = 0

x = 4, x = 12

x can not be 12,

Because 24 - 2(12) = 0

So x = 4

Volume = (24 - 8)(24 - 8)(4)

= 1024