Sphere from volume to curved surface area: The volume of a sphere is 38,808 cm3. Find its curved surface area (in cm2) using π = 22/7.
Aptitude
Volume and Surface Area
Difficulty: Medium
Choose an option
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A5544 sq. cm
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B1386 sq. cm
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C8316 sq. cm
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D4158 sq. cm
Answer
Correct Answer: 5544 sq. cm
Explanation
Introduction / Context:Given volume, we find the radius, then compute curved surface area (CSA). Using π = 22/7 simplifies to integer-friendly values in many classic problems.
Given Data / Assumptions:
- V = 38,808 cm3, π = 22/7
- Sphere: V = (4/3) * π * r^3, CSA = 4 * π * r^2
Concept / Approach:
- Solve r from V, then compute CSA.
Step-by-Step Solution:
(4/3) * (22/7) * r^3 = 38808 ⇒ r^3 = 38808 * 3 / (4 * 22/7) = 9261.r = cube_root(9261) = 21 cm.CSA = 4 * (22/7) * r^2 = 4 * (22/7) * 441 = (88/7) * 441 = 88 * 63 = 5544 cm2.Verification / Alternative check:
Compute 21^3 = 9261; back-substitution gives the original volume.Why Other Options Are Wrong:
- 1386/4158/8316: Do not equal 4πr^2 for r = 21 and π = 22/7.
Common Pitfalls:
- Using 3.14 for π here yields small rounding differences; the question expects 22/7.
- Mixing up CSA with total surface area (same for sphere) is fine, but arithmetic must match.
Final Answer:
5544 sq. cm