Question

the radius of a quarter circle is 17 yards. what is the quarter circles area?
r=17 yd
round your answer to the nearest hundredth.
square yards

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 fraction of the circle

Since we are dealing with a quarter - circle, the area of the quarter - circle will be \( \frac{1}{4} \) of the area of the full circle. So the formula for the area of a quarter - circle \( A_{quarter} \) is \( A_{quarter}=\frac{1}{4}\pi r^2 \).

Step3: Substitute the given radius

We are given that the radius \( r = 17 \) yards. Substitute \( r = 17 \) into the formula for the area of the quarter - circle:
\( A_{quarter}=\frac{1}{4}\times\pi\times(17)^2 \)
First, calculate \( 17^2=289 \). Then the formula becomes \( A_{quarter}=\frac{1}{4}\times\pi\times289 \)
\( A_{quarter}=\frac{289\pi}{4} \)

Step4: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have:
\( A_{quarter}=\frac{289\times3.14159}{4}=\frac{907.92451}{4} = 226.9811275 \)

Step5: Round to the nearest hundredth

Rounding \( 226.9811275 \) to the nearest hundredth gives \( 226.98 \)

Answer:

\( 226.98 \) square yards