The total surface area of a solid hemisphere is 4158 cm2. Find its volume (in cm3).
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 19404.
Given that
The total surface area of a solid hemisphere is 4158 cm2
The total surface area of a hemisphere = 3πr2
Volume of a solid hemisphere = (2/3)πr3 cubic units
where r is the radius of the hemisphere
⇒ 3πr2 = 4158
⇒ 3 × (22/7) × r2 = 4158
⇒ r2 = 4158 × 7/66 = 441
⇒ r = 21 cm
Hence, Volume of a solid hemisphere = (2/3)πr3 = (2/3) × (22/7) × 213 = 19404 cm3