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 \( \pi \).


Answer :




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

\( = \ \frac{1}{3} \pi r^2 h \ + \ \frac{2}{3} \pi R^3 \)

\( = \ \frac{1}{3} \pi r^2 \ × \ r \ + \ \frac{2}{3} \pi r^3 \) [\(\because \) h = r and R = r]

\( = \ \frac{ \pi}{3}r^3(1 \ + \ 2) \ = \ \pi r^3 \)

\( = \ \pi(1)^3 \ = \ \pi \) cm3 [\(\because \) r = 1 cm]

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