SOLUTION: A rectangular solid (with a square base) has a surface area of 121.5 square centimeters. Find the dimensions that will result in a solid with maximum volume.

Question 1125333: A rectangular solid (with a square base) has a surface area of 121.5 square centimeters. Find the dimensions that will result in a solid with maximum volume.
Answer by Aaleia(1) (Show Source): You can put this solution on YOUR website!
Original Poster here and I got it already so no worries! Heres the work.
Let x = the side of the square base and y = height
Let V = volume = x2y
The surface area = 2x2 + 4xy = 121.5

Solve surface area equation for y = (121.5 - 2x2)/4x and sub this into the volume equation

V = x2(121.5 - 2x2)/4x = x(121.5 - 2x2)/4

derivative of V with respect to x = (x/4)(-2x) + (1/4)(121.5 - 2x2) = 0 at the maximum

(1/4)(-4x2 + 121.5 - 2x2) = 0
6x2 = 121.5
x2 = 20.25
x = 4.5
y = (121.5 - 40.5)/(4 * 4.5) =81/18 = 4.5 -> max volume with side 4.5

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