Question

Mr. Aba builds a circular patio with a diameter of 12 feet. He covers the patio with paving stones. The cost of the paving stone is $10.50 a square foot. To the nearest dollar, how much do the paving stones cost.A. $126.00B. $378.00C. $1,187D. $4,748Jacob chose D as the correct answer. How might he have gotten that answer?

Answer 1

Firstly, we are going to obtain the area of the circular patio.

$\begin{gathered} A=\frac{\pi d^2}{4} \\ d\colon\text{diameter} \end{gathered}$$\begin{gathered} A=\frac{3.142\times12^2}{4} \\ A=113.112ft^2 \end{gathered}$

If a paving stone cost $10.50 per square foot, then the total cost of the paving stones will cost:

$\begin{gathered} C=113.112\times10.50 \\ C=\text{\ 1,187.67} \end{gathered}$

Hence, the correct option is Option C

Jacob mistook the given diameter of 12feet to be the radius.

He used the formula of the circular patio to be:

$\begin{gathered} A=\pi r^2 \\ A=3.142\times12^2 \\ A=452.448ft^2 \end{gathered}$

He then multiplied this area by the cost of $10.50, which is equal to:

$\begin{gathered} C=452.448\times10.50 \\ C=\text{ \ 4,750} \end{gathered}$