Question

A solid is in the shape of a cone surmounted on a hemisphere. The radius of each of them being 3.5 cm and the total height of the solid is 9.5 cm. Find the volume of the solid.

Answer 1

We have,

Radius of cone = radius of hemisphere = r = 3.5 cm or AD = BD = CO

Total height of the solid, OC = 9.5 cm 

⇒ OD + CD = 9.5

⇒ OD + 3.5 = 9.5 

⇒ OD = 6 cm

⇒ Height of cone, h = 6 cm

Now,

Volume of solid = Volume of cone + Volume of hemisphere

= `1/3 πr^2h + 2/3 πr^3`

= `1/3 πr^2 (h + 2r)`

= `1/3 xx 22/7 xx 3.5 xx 3.5 xx (6 + 2 xx 3.5)`

= `1/3 xx 22/7 xx 3.5 xx 3.5 xx (6 + 7)`

= `1/3 xx 22/7 xx 3.5 xx 3.5 xx 13`

= `500.5/3`

= 166.83 cm³ 

So, the volume of the solid is 166.83 cm^3. 

Answer 2

Given,

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 the hemisphere = 3.5 cm

Height of cone, h 

= Total height of the solid – Height of hemisphere

= (9.5 – 3.5) cm

= 6 cm

Volume of solid = Volume of cone + Volume of hemisphere

= `1/3 πr^2h + 2/3 πr^3`

= `1/3 πr^2 (h + 2r)`

= `1/3 xx 22/7 xx (3.5)^2 xx (6 + 2 xx 3.5)`

= `1/3 xx 22/7 xx 3.5 xx 3.5 xx (6 + 7)`

= `1/3 xx 22/7 xx 3.5 xx 3.5 xx 13`

= `1/3 xx 22 xx 0.5 xx 3.5 xx 13`

= `500.5/3`

= 166.83 cm³   ...(Approx.)

Hence, the volume of the solid is 166.83 cm³.