Question

9. A solid right circular cone of diameter 14 cm and height 4 cm is melted to form a hollow hemisphere. If the external diameter of the hemisphere is 10 cm, find its internal diameter. Also find the total curved surface area of the hemisphere.

Answer 1

Diameter of the solid cone = 14 cm

radius of the solid cone , r = 7 cm

Height , h = 4 cm

volume of solid cone = 13πr2h = 13π(7)2 (4) = 196π3 cm3Let d1 = external diameter of the hollow hemisphere = 10 cmnow, r1 = external radius of the hemisphere = 5 cmLet r2 = internal radius of the hollow hemispherevolume of hollow hemisphere = 23π[r13 − r23] = 23π [125 − r23] cm3πnow, volume of solid cone = volume of hollow hemisphere⇒196π3 = 23π [125 − r23]⇒98 =125 − r23⇒ r23 = 27⇒r2 = 3 cmnow, internal diameter , d2 = 6 cmTSA of hollow hemisphere = 2πr12 + 2πr22 + π[r12 − r22] = 50 π + 18π + 16π = 84π = 84 ×227 =264 cm2