Q42 of 56 Page 13

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 solid is 9.5 cm. find the volume of the solid. (CBSE 2012)

We have


Given: radius of hemisphere as well as cone (r) = 3.5 cm, height of the solid = 9.5 cm


Height of cone = height of solid – height of hemisphere


⇒ height of the cone = height of solid – radius of hemisphere [∵, height of the cone = hemisphere of the cone]


⇒ height of the cone (h) = 9.5 – 3.5 = 6 cm


Volume of the solid = Volume of the hemisphere + Volume of the cone


⇒ Volume of the solid =


⇒ Volume of the solid =


Thus, volume of the solid is 166.83 cm3.

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