Question

the radius of a quarter circle is 2 feet. what is the quarter circles area? round your answer to the nearest hundredth. square feet

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: Determine the fraction of the circle for a quarter circle.

A quarter circle is \( \frac{1}{4} \) of a full circle. So, the area of a quarter circle will be \( \frac{1}{4} \) of the area of the full circle.

Step3: Substitute the radius into the formula for the quarter - circle area.

We are given that the radius \( r = 2 \) feet. First, calculate the area of the full circle: \( A_{full}=\pi r^{2}=\pi(2)^{2}=4\pi \) square feet. Then, the area of the quarter - circle \( A_{quarter}=\frac{1}{4}\times A_{full}=\frac{1}{4}\times4\pi=\pi \) square feet. If we use \( \pi\approx3.14159 \), then \( A_{quarter}\approx3.14 \) square feet (rounded to the nearest hundredth).

Answer:

\( 3.14 \)