The radius of a metallic spherical ball is 3 cm. If the metallic ball is melted and recast into x number of hemispheres of radius equal to half the radius of the metallic spherical ball, then find the value of x.
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 16.
Volume of sphere = 4/3πr13
here, r1 = radius of sphere = 3 cm
Volume of hemisphere = 2/3πr23
here, r2 = radius of hemisphere = 3/2 cm
4/3πr13 = x × 2/3πr23
⇒ 2 × 33 = x × (3/2)3
⇒ 2 × 27 = x × 27/8
⇒ x = 16