A rectangular box with a square bade is to be formed from a square piece of meta

ID: 2834318 • Letter: A

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A rectangular box with a square bade is to be formed from a square piece of metal with 36 inch sides. If a square piece with side x is cut from each corner of the metal and the sides are folded up to form an open box, the volume if the box is v-=(36-2x)x. Wha value of x will max the volume of th box A rectangular box with a square bade is to be formed from a square piece of metal with 36 inch sides. If a square piece with side x is cut from each corner of the metal and the sides are folded up to form an open box, the volume if the box is v-=(36-2x)x. Wha value of x will max the volume of th box

Explanation / Answer

Let x be the side of the square to remove. The volume of the box is:

V(x) = (36-2x)x = 36x - 2x^2

To find the maximum volume, differentiate and set to 0:

V'(x) = 36 - 4x

0 = 9

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A rectangular box with a square bade is to be formed from a square piece of meta

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