A metallic sphere of volume 3136π cm3 is melted and then recast into smaller cones each of radius 3.5 cm and height 4 cm. How many cones are obtained ?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e. 192.
Given that, volume of sphere = 3136π cm3
Radius of cone = 3.5 cm
Height of cone = 4 cm
Let the number of smaller cones that can be formed by recasting the sphere be n.
According to the given question,
Volume of sphere = n × volume of cone
⇒ 3136π = n × (1/3)πr2h'
⇒ 3136 = (n/3) × (3.5)2 × 4
⇒ n = 64 × 3
⇒ n = 192