A hemisphere of lead of radius 5 cm is cast into a right circular cone of height 75 cm. If the volume of cone and hemisphere are equal, then what will be the radius of the base of the cone?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is Option 1 i.e. 1.8 cm.
When a 2-D figure is recast into another 3-D figure then, their volume must be the same
The volume of the cone = The volume of the hemisphere
⇒ 1/3 × π × R × R × 75 = 2/3 × π × 5 × 5 × 5
⇒ R2 × 25 = 250/3
⇒ R2 = 10/3 = 3.34
⇒ R = √3.33 = 1.8 cm