Question
A circle has a radius of 7
centimeters (cm).
What is the approximate area of the circle?
Use the approximation of 227
for π
in your calculations.
Responses
22
cm2
22 textsf cm squared
14
cm2
14 textsf cm squared
154
cm2
154 textsf cm squared
44
cm2
centimeters (cm).
What is the approximate area of the circle?
Use the approximation of 227
for π
in your calculations.
Responses
22
cm2
22 textsf cm squared
14
cm2
14 textsf cm squared
154
cm2
154 textsf cm squared
44
cm2
Answers
Answered by
GPT-4o mini
To find the area of a circle, you can use the formula:
\[
\text{Area} = πr^2
\]
where \( r \) is the radius of the circle.
Given:
- Radius \( r = 7 \) cm
- \( π \approx \frac{227}{100} \) (or 3.14)
First, calculate \( r^2 \):
\[
r^2 = 7^2 = 49
\]
Now, substitute \( r^2 \) and the approximation of \( π \) into the area formula:
\[
\text{Area} \approx \frac{227}{100} \times 49
\]
Calculating this:
\[
\text{Area} \approx \frac{227 \times 49}{100}
\]
Calculating \( 227 \times 49 \):
\[
227 \times 49 = 11123
\]
Now divide by 100:
\[
\text{Area} \approx \frac{11123}{100} = 111.23 \, \text{cm}^2
\]
Rounding to the nearest whole number, the area is approximately 111 cm².
However, from the provided options, the closest area is:
- 154 cm²
None of the provided options is a perfect match to the calculated area; thus, it appears there may be an error given the context. Based on the calculations, the area of the circle with a 7 cm radius and \( π \approx \frac{227}{100} \) is indeed approximately 111 cm², but the provided option closest in the calculation itself would need to be revised or reconsidered.
\[
\text{Area} = πr^2
\]
where \( r \) is the radius of the circle.
Given:
- Radius \( r = 7 \) cm
- \( π \approx \frac{227}{100} \) (or 3.14)
First, calculate \( r^2 \):
\[
r^2 = 7^2 = 49
\]
Now, substitute \( r^2 \) and the approximation of \( π \) into the area formula:
\[
\text{Area} \approx \frac{227}{100} \times 49
\]
Calculating this:
\[
\text{Area} \approx \frac{227 \times 49}{100}
\]
Calculating \( 227 \times 49 \):
\[
227 \times 49 = 11123
\]
Now divide by 100:
\[
\text{Area} \approx \frac{11123}{100} = 111.23 \, \text{cm}^2
\]
Rounding to the nearest whole number, the area is approximately 111 cm².
However, from the provided options, the closest area is:
- 154 cm²
None of the provided options is a perfect match to the calculated area; thus, it appears there may be an error given the context. Based on the calculations, the area of the circle with a 7 cm radius and \( π \approx \frac{227}{100} \) is indeed approximately 111 cm², but the provided option closest in the calculation itself would need to be revised or reconsidered.