Question

the radius of a quarter circle is 18 miles. what is the quarter circles area? r=18 mi round your answer to the nearest hundredth. square miles

Explanation:

Step1: Recall the area formula for a full 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: Calculate the area of the full circle with \( r = 18 \) miles

Substitute \( r = 18 \) into the formula: \( A_{\text{full}}=\pi\times(18)^2=\pi\times324 = 324\pi \) square miles.

Step3: Find the area of the quarter circle

A quarter circle is \( \frac{1}{4} \) of a full circle, so the area of the quarter circle \( A_{\text{quarter}}=\frac{1}{4}\times A_{\text{full}} \).
Substitute \( A_{\text{full}} = 324\pi \) into the formula: \( A_{\text{quarter}}=\frac{1}{4}\times324\pi = 81\pi \).

Step4: Compute the numerical value and round to the nearest hundredth

Using \( \pi\approx3.14159 \), we have \( 81\pi\approx81\times3.14159 = 254.46939 \).
Rounding to the nearest hundredth (two decimal places), we get \( 254.47 \).

Answer:

254.47