UPSKILL MATH PLUS

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### 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

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

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

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.