Question

the radius of a quarter circle is 9 meters. what is the quarter circles area?
r=9 m
round your answer to the nearest hundredth.
square meters
submit

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 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 \( A_{quarter}=\frac{1}{4}\pi r^2 \).
We know that \( r = 9\) meters. Substitute \( r = 9\) into the formula:
\( A_{quarter}=\frac{1}{4}\times\pi\times(9)^2=\frac{1}{4}\times\pi\times81=\frac{81\pi}{4}\)

Step3: Compute the numerical value

Using \( \pi\approx3.14159\), we have:
\( \frac{81\times3.14159}{4}=\frac{254.46979}{4} = 63.6174475\)

Step4: Round to the nearest hundredth

Rounding \( 63.6174475\) to the nearest hundredth (two decimal places), we look at the third decimal place which is 7. Since \( 7>5\), we round up the second decimal place. So \( 63.6174475\approx63.62\)

Answer:

\( 63.62 \)