A rectangular box with a square bade is to be formed from a square piece of meta
ID: 2834318 • Letter: A
Question
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 boxExplanation / 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