A right circular cone has curved surface area (lateral area) 99 cm² and slant height 9 cm. Find its diameter in centimetres.
Aptitude
Area
Difficulty: Easy
Choose an option
-
A3.5
-
B7
-
C14
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D10.5
Answer
Correct Answer: 7
Explanation
Introduction / Context:The curved surface area (CSA) of a right circular cone is CSA = π * r * l, where r is the base radius and l is the slant height. Given CSA and l, we can recover r and then the diameter 2r.
Given Data / Assumptions:
- CSA = 99 cm²
- Slant height l = 9 cm
Concept / Approach:Compute r = CSA / (π * l). Using π = 22/7 yields an exact value here. Then diameter D = 2r.
Step-by-Step Solution:
r = 99 / (π * 9) = 99 / (9 * 22/7) = 99 * 7 / 198 = 3.5 cmDiameter D = 2 * 3.5 = 7 cmVerification / Alternative check:CSA back-check: π * r * l = (22/7) * 3.5 * 9 = (22/7) * 31.5 = 99 cm², consistent.
Why Other Options Are Wrong:3.5 is the radius (not diameter); 10.5 and 14 assume incorrect r; 7 is the correct diameter.
Final Answer:7