Multiple choice

A hemisphere of lead of diameter 14 cm is cast into a right circular cone of height 14 cm. The radius of the base of the cone is:

  1. 28 cm

  2. 21 cm

  3. 7 cm

  4. 14 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Hemisphere volume = (2/3)πr³ = (2/3)π(7)³ = (686/3)π cm³. Cone volume = (1/3)πR²h = (1/3)πR²(14) = (14/3)πR² cm³. Equating: (686/3)π = (14/3)πR² → 686 = 14R² → R² = 49 → R = 7cm.

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