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Answer :
To find the area of a circle given that its circumference is 35 cm, we'll follow these steps:
1. Understand the formulas:
- The formula for the circumference of a circle is [tex]\( C = 2 \pi r \)[/tex], where [tex]\( C \)[/tex] is the circumference and [tex]\( r \)[/tex] is the radius.
- The formula for the area of a circle is [tex]\( A = \pi r^2 \)[/tex].
2. Find the radius:
- We start with the circumference formula: [tex]\( 35 = 2 \pi r \)[/tex].
- Solve for [tex]\( r \)[/tex] (radius) by dividing both sides by [tex]\( 2\pi \)[/tex]:
[tex]\[
r = \frac{35}{2\pi}
\][/tex]
3. Calculate the radius:
- Using a calculator, you find [tex]\( \pi \approx 3.14159265 \)[/tex].
- So, [tex]\( r = \frac{35}{2 \times 3.14159265} \approx 5.570 \, \text{cm} \)[/tex].
4. Calculate the area:
- Now, use the area formula: [tex]\( A = \pi r^2 \)[/tex].
- Substitute the radius you calculated:
[tex]\[
A = \pi \times (5.570)^2
\][/tex]
- This calculates to approximately [tex]\( A = 97.482 \, \text{cm}^2 \)[/tex].
5. Round the area:
- Round the result to three significant figures: [tex]\( 97.5 \, \text{cm}^2 \)[/tex].
So, the area of the circle is approximately 97.5 cm², correct to three significant figures.
1. Understand the formulas:
- The formula for the circumference of a circle is [tex]\( C = 2 \pi r \)[/tex], where [tex]\( C \)[/tex] is the circumference and [tex]\( r \)[/tex] is the radius.
- The formula for the area of a circle is [tex]\( A = \pi r^2 \)[/tex].
2. Find the radius:
- We start with the circumference formula: [tex]\( 35 = 2 \pi r \)[/tex].
- Solve for [tex]\( r \)[/tex] (radius) by dividing both sides by [tex]\( 2\pi \)[/tex]:
[tex]\[
r = \frac{35}{2\pi}
\][/tex]
3. Calculate the radius:
- Using a calculator, you find [tex]\( \pi \approx 3.14159265 \)[/tex].
- So, [tex]\( r = \frac{35}{2 \times 3.14159265} \approx 5.570 \, \text{cm} \)[/tex].
4. Calculate the area:
- Now, use the area formula: [tex]\( A = \pi r^2 \)[/tex].
- Substitute the radius you calculated:
[tex]\[
A = \pi \times (5.570)^2
\][/tex]
- This calculates to approximately [tex]\( A = 97.482 \, \text{cm}^2 \)[/tex].
5. Round the area:
- Round the result to three significant figures: [tex]\( 97.5 \, \text{cm}^2 \)[/tex].
So, the area of the circle is approximately 97.5 cm², correct to three significant figures.
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