### A 288 cu ft pool is to have a square top.the sides are to be made of glass and the bottom mosaic – dimensions?

a 288 cu ft pool is to have a square top.the sides are to be made of glass and the bottom mosaic. the cost per unit area of glass is 3 times the cost of the mosaic. find the dimensions of the pool having minimum cost.

StoneHenge

on November 30th, -0001

V=ha^2=288. h=288/a^2

A= 4ah +a^2

C=12ah + a^2= (12a288/a^2)+a^2

Take the derivative of C with respect to a, set equal to 0, and get after simplification a^3= 1728 or a =12 which substituted in the first equation gives h=2.

Answer = 12x12x2

Cost=432 which is what you can get no lower than.

Sorry about not showing how the derivative was taken, tough typography, but look at source below.

Cat

on November 30th, -0001

Depends on how deep you want the pool….a 16ft X16 ft pool that is .89 feet would be cheap…….A 16.97ft X16.97ft pool that is .2 inches deep would be even cheaper