A solid metallic sphere of radius 21 cm is melted and moulded into small right circular cones, each of radius 7 cm and height of 3 cm. The number of such cones is:

Question

Question

This question was previously asked in

SSC GD Constable (2022) Official Paper (Held On : 27 Jan 2023 Shift 2)

Answer 1

Given:

Radius of sphere = 21 cm

Radius of the base of small cones = 7 cm

Height of small cones = 3 cm

Formula used:

Volume of sphere = (4/3) × π × r³

Volume of cone = (1/3) × π × r² × h

Where r = radius and h = height of cone

Calculation:

Let the number of small cones = N

The volume of each small cone × N = The volume of the sphere

⇒ N × (1/3) × π × r2 × h = (4/3) × π × r3

⇒ N × (7)² × 3 = 4 × (21)³

⇒ N = 4 × 3 × 3 × 7

⇒ N = 252

∴ The correct answer is 252.

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