Question

a flower garden is in the shape of a circle. the circumference of the garden is 20 meters. what is the area of the garden? use 3.14 for π and round your answer to the nearest whole number.
options:
314 m²
32 m²
127 m²
40 m²

Explanation:

Step1: Recall circumference formula

The formula for the circumference \( C \) of a circle is \( C = 2\pi r \), where \( r \) is the radius. We know \( C = 20 \) meters and \( \pi = 3.14 \). First, solve for \( r \).
\( 20 = 2\times3.14\times r \)
\( 20 = 6.28r \)
\( r=\frac{20}{6.28}\approx3.18 \) meters.

Step2: Recall area formula

The formula for the area \( A \) of a circle is \( A=\pi r^{2} \). Now substitute \( r\approx3.18 \) and \( \pi = 3.14 \) into the formula.
\( A = 3.14\times(3.18)^{2} \)
First, calculate \( (3.18)^{2}\approx10.11 \)
Then, \( A = 3.14\times10.11\approx31.75 \approx 32 \) square meters.

Answer:

B. \( 32\space m^{2} \)