A solid metal cone of height 24 cm and base radius 3.5 cm is melted and recast into small spherical balls of radius 1 cm. How many balls are formed?
Show answer & explanation
Correct answer: B
Explanation
Given:
Height of the cone = 24 cm
Radius of the cone = 3.5 cm
Radius of the small ball = 1 cm
By the formula:
Volume of the cone = (1/3)πr²h
Volume of the sphere = (4/3)πr³
Volume of the cone = (1/3) × π × (3.5)² × 24 = 98π
Volume of a sphere = (4/3) × π × 1³ = (4/3)π
Number of balls = 98π ÷ ((4/3)π) = 73