Question

A solid is in the shape of a hemisphere surmounted by a cone. If the radius
of hemisphere and base radius of cone is 7 cm and height of cone is 3.5 cm,
find the volume of the solid.

Answer 1

Volume of the solid = 2/3 πr3 + 1/3π r2

Answer 2

Total height of the solid= 9.5 cm

Radius of the cone = Radius of the hemisphere = r = 3.5 cm

Radius of the hemisphere = height of hemisphere = 3.5 cm

Height of cone,( h) =total height of the solid - height of hemisphere

h= 9.5- 3.5 cm

h of cone =6cm

Volume of solid = volume of cone + volume of hemisphere

= 1/3πr²h+2/3πr³

= 1/3πr²(h+2r)

= 1/3×22/7×3.5×3.5×(6+2×3.5)

= 1/3×22/7×3.5×3.5×(6+7)

= 1/3×22/7×3.5×3.5×(13)

= 1/3×22×.5×3.5×(13)

= 500.5/3

= 166.83 cm³

Hence, the volume of the solid is 166.83 cm³

hope it is helpful for u