Question
If the area of a circle is 372 cm^2, then what is the length of the diameter? Round to the nearest whole number.
__ cm
__ cm
Answers
Answered by
GPT-4o mini
To find the diameter of a circle given its area, we can use the formula for the area of a circle:
\[
A = \pi r^2
\]
where \( A \) is the area and \( r \) is the radius. We need to solve for the radius first.
Given that the area \( A = 372 \, \text{cm}^2 \):
\[
372 = \pi r^2
\]
First, solve for \( r^2 \):
\[
r^2 = \frac{372}{\pi}
\]
Using \( \pi \approx 3.14 \):
\[
r^2 \approx \frac{372}{3.14} \approx 118.78
\]
Next, take the square root to find \( r \):
\[
r \approx \sqrt{118.78} \approx 10.9 \, \text{cm}
\]
To find the diameter \( d \), we use the relationship:
\[
d = 2r
\]
So,
\[
d \approx 2 \times 10.9 \approx 21.8 \, \text{cm}
\]
Rounding to the nearest whole number gives:
\[
\boxed{22} \, \text{cm}
\]
\[
A = \pi r^2
\]
where \( A \) is the area and \( r \) is the radius. We need to solve for the radius first.
Given that the area \( A = 372 \, \text{cm}^2 \):
\[
372 = \pi r^2
\]
First, solve for \( r^2 \):
\[
r^2 = \frac{372}{\pi}
\]
Using \( \pi \approx 3.14 \):
\[
r^2 \approx \frac{372}{3.14} \approx 118.78
\]
Next, take the square root to find \( r \):
\[
r \approx \sqrt{118.78} \approx 10.9 \, \text{cm}
\]
To find the diameter \( d \), we use the relationship:
\[
d = 2r
\]
So,
\[
d \approx 2 \times 10.9 \approx 21.8 \, \text{cm}
\]
Rounding to the nearest whole number gives:
\[
\boxed{22} \, \text{cm}
\]