The radius as well as the height of a circular cone increases by 10%. The percentage increase in its volume is ______.
Options:
(A) 17.1
(B) 21.0
(C) 33.1
(D) 72.8
Official Answer Key:
C
Step-by-Step Solution & Explanation
Volume V = (1/3)πr²h. If r → 1.1r and h → 1.1h, V_new = (1/3)π(1.1r)²(1.1h) = 1.1³ × V = 1.331 V. Percentage increase = (1.331 − 1) × 100 = 33.1%. Distractor (A) 17.1% comes from adding percentages linearly for one factor only (2×10%+... miscalculated); (D) 72.8% would correspond to (1.1)⁶. Answer: (C) 33.1.
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