The volume of a hemisphere is 32 times the volume of a sphere with a radius of 3 units; the diameter of the hemisphere is ___________ units.
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 24
Given that
The volume of a hemisphere is 32 times the volume of a sphere
the radius of the sphere is r = 3 units
Formula used
The volume of a hemisphere is (2/3)πR3 cubic units
The volume of a sphere is V = 4/3 π r³ cubic units
Calculation
The volume of a hemisphere = 32 × the volume of a sphere
⇒ (2/3)πR3 = 32 × 4/3 π r³
⇒ R3 = 64 r³
⇒ R = 4r = 4 × 3 = 12 units
⇒ Diameter = 2R = 2 × 12 = 24 units
Hence, the diameter of the hemisphere is 24 units