Question

the radius of a circle is 27 inches. what is the circles area?
r=27 in
round your answer to the nearest hundredth.
square inches
submit
work it out
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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

We are given that \( r = 27 \) inches. Substituting \( r = 27 \) into the formula, we get \( A=\pi\times(27)^{2} \).

Step3: Calculate \( 27^{2} \)

First, calculate \( 27^{2}=27\times27 = 729 \). So now the formula becomes \( A=\pi\times729 \).

Step4: Compute the value using \( \pi\approx3.14159 \)

Using the approximation \( \pi\approx3.14159 \), we have \( A = 3.14159\times729 \).
Calculating \( 3.14159\times729 \):
\( 3.14159\times729=3.14159\times(700 + 29)=3.14159\times700+3.14159\times29 \)
\( 3.14159\times700 = 2199.113 \)
\( 3.14159\times29=3.14159\times(30 - 1)=3.14159\times30-3.14159\times1 = 94.2477 - 3.14159 = 91.10611 \)
Adding these two results: \( 2199.113+91.10611 = 2290.21911 \)

Step5: Round to the nearest hundredth

Rounding \( 2290.21911 \) to the nearest hundredth (two decimal places), we look at the third decimal place which is \( 9 \). Since \( 9\gt5 \), we round up the second decimal place. So \( 2290.21911\approx2290.22 \).

Answer:

\( 2290.22 \)