Question

A 273​-ft^3 pool is to be built with a square bottom of side length x. The sides are built with tiles and the bottom with cement. The cost per unit of tiles is ​$77​/ft2 while the cost of the bottom is ​$22​/ft2. Write the total cost C as a function of x.

Answer 1

If the bottom is a square with sides equal to x then, the area is equal to x². The height of the pool is then equal to,
273/x²
Solving for the cost,
sides: (273/x²)(x)(4)(77) = $84084/x
bottoms: x²(22) = 22x²

Adding up all the cost will give us an answer of,
84084/x + 22x²