Radius of a solid hemisphere is 12 cm. If hemisphere is melted to form a cone…
2021
Radius of a solid hemisphere is 12 cm. If hemisphere is melted to form a cone whose base radius is equal to the radius of hemisphere, then what will be the height of cone?
- A.
18 cm
- B.
24 cm
- C.
8 cm
- D.
16 cm
Attempted by 3 students.
Show answer & explanation
Correct answer: B
Volume of hemisphere = (2/3) * π * r³
Volume of cone = (1/3) * π * r² * h
Since the hemisphere is melted to form the cone, their volumes are equal:
(2/3) * π * r³ = (1/3) * π * r² * h
Simplify by canceling (1/3), π, and r² from both sides:
2r = h
Given radius (r) = 12 cm:
h = 2 * 12 = 24 cm.
Final Answer: Option 2 (24 cm)