QA – Placement Quizzes | Mensuration 3D | Question 9

A hollow sphere of internal and external diameters 4 cm and 8 cm respectively is melted into a cone of base diameter 8 cm. The height of the cone is:
(A) 12 cm
(B) 14 cm
(C) 15 cm
(D) 18 cm

Answer: (B)
Explanation: Volume of the hollow sphere = 4/3 * π * (R³-r³) = 4/3 * π * (4³-2³) = 4/3 * π * 56 cm³
Let the height of the cone be h cm. Then,
1/3 * π * 4 * 4 * h = 4/3 * π * 56
h = (4 * 56 / 4 * 4) = 14 cm.
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