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Question
A solid is in the shape of a cone standing on a hemisphere with both their diameters being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid. [Use π = 3.14]
Solution
Diameter of cone (r) = Diameter of hemisphere (r)
Height of cone (h) = Radius of cone = `1/2`cm
Volume of the solid = Volume of the cone + Volume of the hemisphere
= `1/3 πr^2h + 2/3 πr^3`
= `(πr^2)/3 (h + 2r)`
= `π/3(1/2)^2 (1/2 + 2 xx 1/2)`
= `π/(3 xx 4) (3/2) cm^3`
= `3.14/8 cm^3`
∴ Volume of the solid = 0.3925 cm3
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