UPSKILL MATH PLUS

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Learn more### Theory:

Hemisphere:

A section of the sphere cut by a plane through any of its great circles is a hemisphere. In another way, we can say, one half of a sphere is called a hemisphere.

Volume of a hemisphere:

Let \(r\) be the radius of a sphere.

Volume of a hemisphere \(=\) $\frac{1}{2}$ \(\times\) Volume of a sphere

\(=\) $\frac{1}{2}\times \left(\frac{4}{3}\mathrm{\pi}{r}^{3}\right)$

\(=\) $\frac{2}{3}\mathrm{\pi}{r}^{3}$

Volume of a hemisphere \(=\) $\frac{2}{3}\mathrm{\pi}{r}^{3}$ cu. units

Volume of hollow hemisphere (volume of the material used):

Let \(r\) be the inner radius and \(R\) be the outer radius of the hollow hemisphere.

Volume of hollow hemisphere \(=\) Volume of the outer hemisphere \(-\) Volume of the inner hemisphere

\(=\) $\frac{2}{3}\mathrm{\pi}{R}^{3}$ \(-\) $\frac{2}{3}\mathrm{\pi}{r}^{3}$

\(=\) $\frac{2}{3}\mathrm{\pi}\left({R}^{3}-{r}^{3}\right)$

**Volume of a hollow hemisphere**\(=\) $\frac{2}{3}\mathrm{\pi}\left({R}^{3}-{r}^{3}\right)$ cu. units

Important!

The value of \(\pi\) should be taken as $\frac{22}{7}$ unless its value is shared in the problem.