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 the area \( A = 1520 \) square meters, so we can solve for \( r \).
\[
1520=\pi r^{2}
\]
\[
r^{2}=\frac{1520}{\pi}
\]
\[
r = \sqrt{\frac{1520}{\pi}}
\]

Step2: Recall the circumference formula of a circle

The length of the row of bricks is the circumference \( C \) of the circle, and the formula for the circumference of a circle is \( C = 2\pi r \). Substitute \( r=\sqrt{\frac{1520}{\pi}} \) into the circumference formula:
\[
C=2\pi\sqrt{\frac{1520}{\pi}}
\]
Simplify the expression:
\[
C = 2\sqrt{\pi\times1520}
\]
Calculate the value inside the square root: \( \pi\times1520\approx3.14159\times 1520 = 4775.2168 \)
Then \( \sqrt{4775.2168}\approx69.10 \)
And \( C = 2\times69.10 = 138.2 \approx138 \) (rounded to the nearest meter)

Answer:

138