### Theory:

Hemisphere:
A 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

Example:
The radius of the hemisphere is $$14 \ cm$$. Find the volume of the hemisphere in grams if $$1 \ cm^3 = 0.4 \ g$$.

Solution:

Radius of the hemisphere $$(r)$$ $$=$$ $$14 \ cm$$

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

$$=$$ $\frac{2}{3}×\frac{22}{7}×{14}^{3}$

$$=$$ $\frac{2}{3}×\frac{22}{7}×14×14×14$

$$=$$ $$5749.33$$ $$cm^3$$

Now, convert $$cm^3$$ to $$g$$.

$$1 \ cm^3$$ $$=$$ $$0.4 \ g$$

$$5749.33 \ cm^3$$ $$=$$ $$5749.33 \times 0.4$$ $$=$$ $$2299.732 \ g$$

Therefore, the volume of the hemisphere is $$2299.732 \ g$$.
Important!
The value of $$\pi$$ should be taken as $\frac{22}{7}$ unless its value is shared in the problem.