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A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π.

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Answer

Given,

Radius of cone = Radius of hemisphere = r = 1 cm

Height of cone (h) = 1 cm

A solid is in the shape of a cone standing on a hemisphere with both their radii being equal to 1 cm and the height of the cone is equal to its radius. Find the volume of the solid in terms of π. NCERT Class 10 Mathematics CBSE Solutions.

Volume of solid = Volume of cone + Volume of hemisphere

=13πr2h+23πr3=πr23(h+2r)=π×(1)23×(1+2×1)=π×13×(1+2)=π3×3=π cm3.= \dfrac{1}{3}πr^2h + \dfrac{2}{3}πr^3 \\[1em] = \dfrac{πr^2}{3}(h + 2r) \\[1em] = \dfrac{π \times (1)^2}{3} \times (1 + 2 \times 1) \\[1em] = \dfrac{π \times 1}{3} \times (1 + 2) \\[1em] = \dfrac{π}{3} \times 3 \\[1em] = π \text{ cm}^3.

Hence, volume of solid = π cm3.

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