Question

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 7 cm and the height of the cone is equal to its diameter. Find the volume of the solid. [Use`pi22/7`]

Answer 1

Let r and h be radius and height of the cone respectively.

Radius of cone (r) = 7 cm (Given)

Diameter of cone = 2 × r = (2 × 7) cm = 14 cm

According to the question, height of the cone is equal to its diameter.

∴ Height of cone (h) = 14 cm

Radius of hemisphere = Radius of cone = 7 cm

∴ Volume of solid = Volume of cone + Volume of hemisphere

`=1/3pir^2h+2/3pir^3`

`=(pir^2)/3[h+2r]`

`=1/3xx22/7xx7xx7xx[14+(2xx7)]cm^2`

`=22/3xx7xx28cm^3`

`=4312/2cm^2`

`=1437.33cm^3`

Thus, the volume of the solid is 1437.33 cm³.