Question

a garden shop sells 15\ by 15\ square stepping stones for the same price as 20\ round stones. if all stepping stones are the same thickness, which option gives the most rock for the money?
the area of a square stepping stone is (square) in. (^{2}) and the area of a round stepping stone is (square) in. (^{2}), so the option that gives the most rock for the money is the (square) stepping stones.
(type integers or decimals rounded to the nearest tenth as needed.)

Explanation:

Step1: Calculate the area of the square stepping stone

The formula for the area of a square is \(A = s^2\), where \(s\) is the side - length. For a square with \(s = 15\) inches, \(A_{square}=15\times15=225\) in².

Step2: Calculate the area of the round stepping stone

The formula for the area of a circle is \(A=\pi r^2\), where \(r\) is the radius. Given \(d = 20\) inches (diameter), then \(r=\frac{d}{2}=10\) inches. Using \(\pi\approx3.14\), \(A_{circle}=\pi r^2=3.14\times10^2 = 314\) in².

Answer:

The area of the square stepping stone is \(225\) in². The area of the round stepping stone is \(314\) in². The round stepping stones give the most rock for the money.