Multiple choice

The base radius of a solid cylinder is 12 cm and its height is 15 cm. If this solid cylinder is to be melted and recast into ‘n’ number of toys in the form of right circular cone , whose height is 9 cm and it is mounted on a hemisphere of radius 3 cm. Then find the value of ‘n’?

  1. 54

  2. 27

  3. 64

  4. 48
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

When the solid is melted and recast, volume remains constant. Original cylinder volume = π × 12² × 15 = 2160π. Each toy consists of a cone mounted on a hemisphere. Cone volume = (1/3)π × 3² × 9 = 27π. Hemisphere volume = (2/3)π × 3³ = 18π. Total toy volume = 45π. Number of toys n = 2160π/45π = 48.

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