A solid hemisphere of radius 10 cm is melted into two…

A solid hemisphere of radius 10 cm is melted into two cones of equal height. If each cone's redius is 5 cm, what is the height of each cone?

Show answer & explanation

Correct answer: A

Explanation

The correct answer is option 1 i.e. 40 cm.

Volume of a hemisphere = $2\over3$ πr³ = $2\over3$ π(10³) = $2000π\over3$

Volume of one cone = $1\over3$ πr²h = $1\over3$ π(5²)h = $25πh\over3$

Two cones volume = $50πh\over3$

⇒ $2000π\over3$ = $50πh\over3$

⇒ 2000 = 50h

⇒ h = 40 cm

SSC CGL 2025 PYQ — Question 60