Question
circumference of a circle is 23 cm . \( N \) that the area of the circle is \( 42.1 \mathrm{em}^{2} \), correct to 3 significant figures.
Ask by Montgomery Ray. in the United Kingdom
Jan 20,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The area of the circle is 42.1 cm².
Solution
To find the area of a circle given its circumference, follow these steps:
1. **Given:**
- **Circumference (C)** = 23 cm
2. **Find the Radius (r):**
The formula for the circumference of a circle is:
\[
C = 2\pi r
\]
Solving for \( r \):
\[
r = \frac{C}{2\pi} = \frac{23}{2\pi} \approx \frac{23}{6.28319} \approx 3.663 \text{ cm}
\]
3. **Calculate the Area (A):**
The formula for the area of a circle is:
\[
A = \pi r^2
\]
Substituting the value of \( r \):
\[
A = \pi (3.663)^2 \approx \pi \times 13.406 \approx 42.1 \text{ cm}^2
\]
4. **Final Answer:**
The area of the circle is **42.1 cm²** (correct to three significant figures).
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Bonus Knowledge
Did you know that the circumference of a circle can be used to derive the radius and area using simple formulas? The circumference \( C \) is related to the radius \( r \) by the equation \( C = 2\pi r \). With a circumference of 23 cm, you can calculate the radius and use it to find the area! To find the area \( A \), you can use the formula \( A = \pi r^2 \). Once you calculate the radius from the circumference, plug it into the area formula, and you’ll find that the area nearly matches the given value! Just make sure you're rounding properly to hit that three significant figures mark!
