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Question
A solid is in the form of a cone standing on a hemi-sphere with both their radii being equal to 8 cm and the height of cone is equal to its radius. Find, in terms of π, the volume of the solid.
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Solution
Given, Radius of each cone and hemi-sphere (r) = 8 cm
Height of cone (h) = r = 8 cm
∴ Volume of solid
= `1/3pir^2h + 2/3pir^3`
= `1/3pir^2(h + 2r) cm^3`
= `1/3pi xx 8 xx 8(8 + 2 xx 8) cm^3`
= `64/3 pi(8 + 16) cm^3`
= `64/3pi xx 24`
= 512 π cm3
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