Chapter 1.1, Problem 21E

Solution

To find: Which option gives the most rock for the money, square stones of $12\text{'}$ by $12\text{'}$ or $13\text{'}$ round stones.

The square stones give the most rock for the money.

Given Information:

The side of the square is $12\text{'}$ and the diameter of the round stone is $13\text{'}$ .

Concept Used:

The area of square is ${\text{A}}_s\text{= side}\times \text{side}$ .

The area of a circle is $A_c=\pi r^2$ , where $r$ is the radius of the circle.

Calculation:

Since the diameter of the round stone is $13\text{'}$ it implies the radius of the round stone is $\frac{13}{2}$ feet.

Substitute $\frac{13}{2}$ for $r$ into $A_c=\pi r^2$ .

  $\begin{array}{c}{A}_c=\pi {\left(\frac{13}{2}\right)}^2\\ =\pi \left(\frac{169}{4}\right)\\ \approx 132.7{\text{ ft}}^2\end{array}$

Substitute 12 for side into ${\text{A}}_s\text{= side}\times \text{side}$ .

  $\begin{array}{c}{\text{A}}_s\text{= side}\times \text{side}\\ \text{=12}\times 12\\ =144{\text{ ft}}^2\end{array}$

Thus, the area of square stones in more than the area of round stones.

Therefore, the square stones give the most rock for the money.