Question

the circumference of a circle is 27.632 feet. what is the circles area? round your answer to the nearest hundredth. square feet

Explanation:

Step1: Recall formulas for circle

The circumference of a circle is given by \( C = 2\pi r \), and the area is given by \( A=\pi r^{2} \). First, we need to find the radius \( r \) from the circumference.
Given \( C = 27.632 \) feet, from \( C = 2\pi r \), we can solve for \( r \): \( r=\frac{C}{2\pi} \).
Substitute \( C = 27.632 \) and \( \pi\approx3.14 \) (or use a more precise value of \( \pi \)): \( r=\frac{27.632}{2\times3.14}=\frac{27.632}{6.28} = 4.4 \) feet (we can also use a calculator for more precision, if we use \( \pi = 3.1416 \), \( r=\frac{27.632}{2\times3.1416}=\frac{27.632}{6.2832}\approx4.4 \) feet as well).

Step2: Calculate the area

Now that we have the radius \( r = 4.4 \) feet, we use the area formula \( A=\pi r^{2} \).
Substitute \( r = 4.4 \) and \( \pi\approx3.14 \): \( A = 3.14\times(4.4)^{2} \).
First, calculate \( (4.4)^{2}=4.4\times4.4 = 19.36 \).
Then, \( A=3.14\times19.36 = 60.7904 \) square feet.
If we use a more precise value of \( \pi \) (e.g., \( \pi = 3.1416 \)): \( A=3.1416\times(4.4)^{2}=3.1416\times19.36\approx60.79 \) square feet (rounded to the nearest hundredth).

Answer:

\( 60.79 \) square feet (or if we calculate with more precise steps:
First, \( r=\frac{27.632}{2\pi}=\frac{27.632}{2\times3.1416}\approx4.4 \) (exact calculation: \( 27.632\div6.2832\approx4.4 \)). Then \( A = \pi r^{2}=3.1416\times4.4^{2}=3.1416\times19.36 = 60.790336\approx60.79 \) when rounded to the nearest hundredth)