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 formula for the area 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, and we need to find the radius first. So we set up the equation \( 1520=\pi r^2 \). To solve for \( r^2 \), we divide both sides by \( \pi \): \( r^2=\frac{1520}{\pi} \).

Step2: Calculate the radius

Using a calculator, \( \frac{1520}{\pi}\approx\frac{1520}{3.1416}\approx483.83 \). Then, to find \( r \), we take the square root of \( 483.83 \): \( r = \sqrt{483.83}\approx21.996 \) meters (approximately 22 meters).

Step3: Recall the formula for the circumference of a circle

The circumference \( C \) of a circle (which is the length of the row of bricks, as it's the perimeter of the circular plaza) is given by \( C = 2\pi r \). Now we substitute \( r\approx22 \) into the formula.

Step4: Calculate the circumference

\( C = 2\times\pi\times22\approx2\times3.1416\times22\approx138.23 \) meters. If we use the more accurate value of \( r\approx21.996 \), then \( C = 2\times\pi\times21.996\approx2\times3.1416\times21.996\approx138.21 \) meters, which rounds to 138 meters.

Answer:

138