Question
We can use the formula \( r=\sqrt{\frac{S}{12.6}} \) to relate a ball's surface area \( S \) (in square inches) to its radius \( r \) (in inches). Suppose a ball has a surface area of 138.6 square inches. What is its radius? Round your answer to the nearest tenth.
Ask by Burton Tran.
Feb 06,2025 04:34
UpStudy AI Solution
Tutor-Verified Answer
Answer
The radius of the ball is approximately 3.3 inches.
Solution
To find the radius \( r \) of the ball given its surface area \( S = 138.6 \) square inches, we'll use the provided formula:
\[
r = \sqrt{\frac{S}{12.6}}
\]
**Step 1: Plug in the surface area into the formula**
\[
r = \sqrt{\frac{138.6}{12.6}}
\]
**Step 2: Simplify the division**
\[
\frac{138.6}{12.6} = 11
\]
**Step 3: Take the square root**
\[
r = \sqrt{11} \approx 3.3166
\]
**Step 4: Round to the nearest tenth**
\[
r \approx 3.3 \text{ inches}
\]
**Answer:**
The radius of the ball is approximately **3.3 inches**.
Answered by UpStudy AI and reviewed by a Professional Tutor
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Explain 
Simplify this solution Beyond the Answer
To find the radius \( r \), we can plug the surface area \( S = 138.6 \) into the formula:
\[
r = \sqrt{\frac{138.6}{12.6}}
\]
Calculating the fraction gives us:
\[
\frac{138.6}{12.6} = 11
\]
Now, taking the square root:
\[
r = \sqrt{11} \approx 3.31662479
\]
Rounding this to the nearest tenth, the radius \( r \) is approximately \( 3.3 \) inches.
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