Question

the radius of a quarter circle is 12 meters. what is the quarter circle’s area? round your answer to the nearest hundredth. square meters

Explanation:

Step1: Recall the area formula for a circle

The area of a full circle is given by the formula \( A = \pi r^2 \), where \( r \) is the radius of the circle.

Step2: Determine the area of the quarter circle

Since a quarter circle is one - fourth of a full circle, the area of a quarter circle \( A_{quarter} \) is \( \frac{1}{4} \) of the area of the full circle. So the formula for the area of a quarter circle is \( A_{quarter}=\frac{1}{4}\pi r^2 \).
We are given that the radius \( r = 12\) meters. Substitute \( r = 12\) into the formula:
\( A_{quarter}=\frac{1}{4}\times\pi\times(12)^2 \)
First, calculate \( (12)^2=144 \). Then, \( \frac{1}{4}\times144 = 36 \). So the formula becomes \( A_{quarter}=36\pi \).
Using the approximation \( \pi\approx3.14159 \), we have \( A_{quarter}=36\times3.14159 = 113.09724 \).

Step3: Round to the nearest hundredth

Rounding \( 113.09724 \) to the nearest hundredth, we look at the thousandth place digit which is 7. Since \( 7>5 \), we round up the hundredth place digit. So \( 113.09724\approx113.10 \).

Answer:

\( 113.10 \) square meters