Question

the radius of a circle is 28.8 inches. what is the circles area? round your answer to the nearest hundredth. square inches

Explanation:

Step1: Recall the formula for the area of a circle

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

Step2: Substitute the given radius into the formula

Given that the radius \( r = 28.8 \) inches. Substitute \( r = 28.8 \) into the formula: \( A=\pi\times(28.8)^{2} \).

First, calculate \( (28.8)^{2}=28.8\times28.8 = 829.44 \).

Then, \( A=\pi\times829.44 \). Using \( \pi\approx3.14159 \), we get \( A\approx3.14159\times829.44 \).

Step3: Calculate the value

\( 3.14159\times829.44 = 3.14159\times800+3.14159\times29.44 \)
\( = 2513.272+3.14159\times29.44 \)
\( 3.14159\times29.44\approx3.14159\times29 + 3.14159\times0.44\)
\( = 91.10611+1.38230 \)
\( = 92.48841 \)
Then \( 2513.272+92.48841 = 2605.76041 \) (using a calculator directly for \( 3.14159\times829.44 \) gives approximately \( 2605.76 \) when rounded to the nearest hundredth).

Answer:

\( 2605.76 \)