Question
What is the area of a circular mirror with a radius of 10 cm ? A. \( 1256.6 \mathrm{~cm}^{2} \) B. \( 31.4 \mathrm{~cm}^{2} \) C. \( 62.8 \mathrm{~cm}^{2} \) D. \( 314.2 \mathrm{~cm}^{2} \)
Ask by Reed Vega. in the United States
Mar 12,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The area of the circular mirror is approximately \( 314.2 \, \mathrm{cm}^{2} \), so the correct answer is D.
Solution
**Step 1:**
The area \(A\) of a circle is given by the formula
\[
A = \pi r^2
\]
**Step 2:**
Substitute the given radius \( r = 10 \) cm into the formula:
\[
A = \pi \times 10^2 = \pi \times 100 = 100\pi
\]
**Step 3:**
Approximate the area using \( \pi \approx 3.1416 \):
\[
A \approx 100 \times 3.1416 = 314.16 \, \mathrm{cm}^2
\]
**Step 4:**
Compare the result with the given options. The closest match is:
D. \( 314.2 \mathrm{~cm}^{2} \)
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Simplify this solution Bonus Knowledge
To find the area of a circular mirror, you can use the formula for the area of a circle, which is given by \( A = \pi r^2 \), where \( r \) is the radius. With a radius of 10 cm, the area calculates to \( A = \pi (10)^2 = 100\pi \), which equals approximately \( 314.2 \mathrm{~cm}^2 \). So, the correct answer is D. Isn't it fascinating how simple geometry can help us calculate areas so quickly? Just a little bit of π magic, and you're all set! And if you're ever making a round mirror, consider not just the area, but also the shape's aesthetics—the eye of the beholder and all that!
