$A$ 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 $\pi$.
(N/A) Given that,
Height $(h)$ of the conical part $=$ Radius $(r)$ of the conical part $= 1\, cm$.
Radius $(r)$ of the hemispherical part $=$ Radius of the conical part $(r)$ $= 1\, cm$.
Volume of the solid $=$ Volume of the conical part $+$ Volume of the hemispherical part.
Volume of the solid $= \frac{1}{3} \pi r^2 h + \frac{2}{3} \pi r^3$.
Substituting the values:
Volume of the solid $= \frac{1}{3} \pi (1)^2 (1) + \frac{2}{3} \pi (1)^3$.
Volume of the solid $= \frac{1}{3} \pi + \frac{2}{3} \pi = \frac{3}{3} \pi = \pi\, cm^3$.
Height $(h)$ of the conical part $=$ Radius $(r)$ of the conical part $= 1\, cm$.
Radius $(r)$ of the hemispherical part $=$ Radius of the conical part $(r)$ $= 1\, cm$.
Volume of the solid $=$ Volume of the conical part $+$ Volume of the hemispherical part.
Volume of the solid $= \frac{1}{3} \pi r^2 h + \frac{2}{3} \pi r^3$.
Substituting the values:
Volume of the solid $= \frac{1}{3} \pi (1)^2 (1) + \frac{2}{3} \pi (1)^3$.
Volume of the solid $= \frac{1}{3} \pi + \frac{2}{3} \pi = \frac{3}{3} \pi = \pi\, cm^3$.
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