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Question
A solid is in the shape of a right-circular cone surmounted on a hemisphere, the radius of each of them being 7 cm and the height of the cone is equal to its diameter. Find the volume of the solid.
Solution
Given, radius of cone = radius of hemisphere
= r
= 7 cm
Height of cone (h) = 2 × radius
= 2 × 7
= 14 cm
Volume of solid = Volume of cone + Volume of hemisphere
Volume of solid (V) = `1/3 πr^2h + 2/3 πr^3`
= `1/3 πr^2(2r) + 2/3 πr^3` ...(∵ h = 2r)
= `2/3 πr^3 + 2/3 πr^3`
= `4/3 πr^3`
= `4/3 xx 22/7 xx 7 xx 7 xx 7`
= `4312/3`
= 1437.33 cm3
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