QA – Placement Quizzes | Mensuration 3D | Question 7

A metallic hemisphere is melted and recast in the shape of a cone with the same base radius (R) as that of the hemisphere. If H is the height of the cone, then:
(A) H = 2R
(B) H = 3R
(C) H = 2/3R
(D) H = 3/2R

Answer: (A)
Explanation: Volume of the Hemisphere = 2/3 * Pi * R^3
Volume of the Cone = 1/3 * Pi * R^2 * H
As the two volumes are same, we have
2/3 * Pi * R^3 = 1/3 * Pi * R^2 * H
Therefore, H = 2R.
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