A solid right cone of diameter 14 cm and height 4 cm is melted to form a holow hemisphere - Maths - Surface Areas and Volumes

Question

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

Ashutosh Verma · Accepted Answer

Diameter of the solid cone = 14 cm
radius of the solid cone , r = 7 cm
Height , h = 4 cm
volume of solid cone = 13πr2h = 13π72 (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 =
23πr13 - 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 + πr12 - r22 = 50 π + 18π +
16π = 84π = 84 ×227 =264 cm2

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