If the total surface area of a solid hemisphere is 462 cm2, find its volume.
Let the radius of solid sphere be r cm
Total surface area of solid hemisphere = 3πr2
Given, total surface area of solid hemisphere = 462 cm2
∴ 3πr2 = 462 cm2
⇒ 3 × 22/7 × r2 = 462 cm2
⇒ r2 = 462 × 1/3 × 7/22 cm2 = 49 cm2
⇒ r = 7 cm
Volume of solid hemisphere = π r3
= 2/3 × 22/7 × 73 cm3
= 718.67 cm3
∴ Volume of solid hemisphere is 718.67 cm3