A right circular cylinder and a right circular cone have the same base radius 6 cm and the same height 8 cm. Find the ratio of the curved surface area of the cylinder to that of the cone.
Aptitude
Volume and Surface Area
Difficulty: Medium
Choose an option
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A4 : 3
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B8 : 3
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C8 : 5
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D5 : 3
Answer
Correct Answer: 8 : 5
Explanation
Introduction / Context:Curved (lateral) surface area of a cylinder depends on radius and height; for a cone it depends on radius and slant height. With the same radius and height, we compute each and then form the ratio.
Given Data / Assumptions:
- Radius r = 6 cm; height h = 8 cm.
- CSA_cylinder = 2πrh.
- CSA_cone = πrl, where l = √(r^2 + h^2).
Concept / Approach:Compute l, then both CSAs, then the ratio.
Step-by-Step Solution:
l = √(6^2 + 8^2) = √(36 + 64) = √100 = 10CSA_cylinder = 2π * 6 * 8 = 96πCSA_cone = π * 6 * 10 = 60πRatio = 96π : 60π = 8 : 5Verification / Alternative check:Cancel π to simplify; ratio reduces cleanly to 8:5.
Why Other Options Are Wrong:Other ratios do not match the computed CSA values with l = 10.
Common Pitfalls:Using height instead of slant height in the cone’s CSA; forgetting to compute l by Pythagoras.
Final Answer:8 : 5