Multiple choice

The radius and height of a right circular cone are in the ratio 3 : 4 and its volume is 96p cm3. What is its lateral surface area?

  1. 24πcm2.

  2. 36πcm2.

  3. 48π cm2.

  4. 60πcm2.
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D Correct answer
Explanation

Let r=3k, h=4k. Volume = (1/3)πr²h = (1/3)π(9k²)(4k) = 12πk³ = 96π, so k³=8, k=2. Thus r=6 cm, h=8 cm. Lateral surface area = πrl, where l = sqrt(r²+h²) = sqrt(36+64) = 10 cm. LSA = π(6)(10) = 60π cm².

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