Question

a circular city plaza is surrounded by a row of bricks. the area of the plaza is 1,520 square meters. how long is the row of bricks, to the nearest meter? type the answer in the box. meters

Explanation:

Step1: Recall the area formula of a circle

The area \( A \) of a circle is given by the formula \( A=\pi r^{2} \), where \( r \) is the radius of the circle. We know that \( A = 1520 \) square meters. So we can solve for \( r \) first.
\[
r^{2}=\frac{A}{\pi}=\frac{1520}{\pi}
\]
\[
r=\sqrt{\frac{1520}{\pi}}
\]

Step2: Recall the circumference formula of a circle

The length of the row of bricks (which is the circumference \( C \) of the circular plaza) is given by the formula \( C = 2\pi r \). Substitute \( r=\sqrt{\frac{1520}{\pi}} \) into the circumference formula:
\[
C=2\pi\sqrt{\frac{1520}{\pi}}=2\sqrt{\pi\times1520}
\]
First, calculate \( \pi\times1520\approx3.1416\times 1520 = 4775.232 \)
Then, \( \sqrt{4775.232}\approx69.1 \)
Then, \( C = 2\times69.1=138.2\approx138 \) (to the nearest meter)

Answer:

138