Hello, ClutchUSMC!

You are putting in a 20ft x 30ft rectangular pool.

Your pool will be surrounded by a concrete sidewalk of uniform width and 3 inches thick.

Write an expression in terms of $\displaystyle x$ for the volume of concrete in the sidewalk.

Explain how you got your expression. I assume that $\displaystyle x$ is the width of the sidewalk. Code:

: x : - 30 - : x :
- * - - - - - - - - * - -
x | | :
- | * - - - - * | :
: | | | | :
20 | |20 | | 20+2x
: | | 30 | | :
- | * - - - - * | :
x | | :
- * - - - - - - - - * - -
: - - 30+2x - - :

The total area is: .$\displaystyle (30+2x)(20+2x) \:=\:600 + 100x + 4x^2$ ft²

The pool area is: .$\displaystyle 30 \times 20 \:=\: 600$ ft²

The area of the sidewalk is: .$\displaystyle (600 + 100x + 4x^2) - 600 \:=\:100x + 4x^2$ ft²

The thickness of the sidewalk is: .$\displaystyle 3\text{ inches }=\:\frac{1}{4}\text{ ft}$

Therefore, the volume of the concrete is: .$\displaystyle V \;=\;\frac{1}{4}(100x + 4x^2) \;=\;25x + x^2$ ft³