Question

determine the dimensions of a rectangular solid (with a square base) with maximun volume if its surface area is 337.5 square centimeters.

Answer 1

Volume V = a^2h where a = length of a side of the base and h = height
surface area 2a^2 + 4ah = 337.5
from this h = (337.5 - 2a^2) / 4a

therefore the volume
V = a^2(337. 5 - 2a^2) / 4a

V = 0.25a(337.5 - 2a^2)
V = 84.375 - 0.5a^3

Answer 2

now find dV/da and equate to 0
solve for a and then find h

validate that this is a maximum

Answer 3

oops sorry theres an error in the last line
correct is
V = 84.375a - 0.5a^3