Question

a middle school has an oval track with the dimensions shown. what is the distance around the track? use 3.14 for π. show your work. lisa helps her aunt build a circular patio with a diameter of 12 feet. they cover the patio with paving stones. the cost of the paving stones is $10.50 per square foot. to the nearest dollar, how much do the paving stones cost? a $126 b $396 c $1,187 d $4,748 jacob chose d as the correct answer. how might he have gotten that answer?

Explanation:

Step1: Find the area of the circular patio

The formula for the area of a circle is $A=\pi r^{2}$, where $r$ is the radius. Given the diameter $d = 12$ feet, the radius $r=\frac{d}{2}=\frac{12}{2}=6$ feet. Substituting $r = 6$ and $\pi=3.14$ into the formula, we get $A = 3.14\times6^{2}=3.14\times36 = 113.04$ square - feet.

Step2: Calculate the total cost

The cost per square - foot is $\$10.50$. Multiply the area by the cost per square - foot: $113.04\times10.50 = 1186.92\approx1187$.

Answer:

C. $1,187$
To answer how Jacob might have gotten D as the answer: He might have used the diameter instead of the radius in the area formula. If he used $A=\pi d^{2}$ with $d = 12$ and $\pi = 3.14$, then $A=3.14\times12^{2}=3.14\times144 = 452.16$. Then multiplying by the cost per square - foot $10.50$, we get $452.16\times10.50=4747.68\approx4748$.