Question

question 5 of 9
find the area of a circle with radius 20.8 ft, both in terms of \\(\pi\\) and to the nearest tenth. use 3.14 for \\(\pi\\).
\\(\bigcirc\\) \\(a = 1,730.56\pi\\,\text{ft}^2 \approx 5434\\,\text{ft}^2\\)
\\(\bigcirc\\) \\(a = 41.6\pi\\,\text{ft}^2 \approx 130.6\\,\text{ft}^2\\)
\\(\bigcirc\\) \\(a = 432.64\pi\\,\text{ft}^2 \approx 1358.5\\,\text{ft}^2\\)
\\(\bigcirc\\) \\(a = 83.2\pi\\,\text{ft}^2 \approx 261.2\\,\text{ft}^2\\)

Explanation:

Step1: Recall the formula for the area of a circle

The formula for the area \( A \) of a circle is \( A = \pi r^2 \), where \( r \) is the radius of the circle.

Step2: Calculate the area in terms of \( \pi \)

Given that the radius \( r = 20.8 \) ft. Substitute \( r = 20.8 \) into the formula:
\( A=\pi\times(20.8)^2 \)
First, calculate \( 20.8^2 = 20.8\times20.8 = 432.64 \)
So, \( A = 432.64\pi \) square feet.

Step3: Calculate the numerical value using \( \pi = 3.14 \)

Substitute \( \pi = 3.14 \) into \( A = 432.64\pi \):
\( A=432.64\times3.14 \)
Calculate \( 432.64\times3.14 = 1358.4896 \approx 1358.5 \) square feet (to the nearest tenth).

Answer:

A = 432.64π ft² ≈ 1358.5 ft² (the third option: A = 432.64π ft² ≈ 1358.5 ft²)