Question

How many $\mathrm{liters}$ of milk can a hemispherical bowl of diameter $10.5\mathrm{cm}$hold? (Assume $\mathrm{\pi }=\frac{22}{7}$)

Answer 1

Step 1: Find the radius of hemispherical bowl

Given: Diameter of hemispherical bowl $=10.5\mathrm{cm}$

So, Radius of hemispherical bowl is half of diameter,

$\Rightarrow \mathrm{r}=\frac{10.5}{2}$

$\Rightarrow \mathrm{r}=5.25\mathrm{cm}$

Step 2: Find the capacity of hemispherical bowl

As, Volume of a hemisphere $=\frac{2}{3}{\mathrm{\pi r}}^3$

Volume of the given hemispherical bowl $=\left(\frac{2}{3}\right)\left(\frac{22}{7}\right){\left(5.25\right)}^3$ $\left[\because \mathrm{\pi }=\frac{22}{7}\right]$

$=303.1875{\mathrm{cm}}^3$

Since, $1\mathrm{liter}=1000{\mathrm{cm}}^3$

$\Rightarrow$ $1{\mathrm{cm}}^3=\frac{1}{1000}\mathrm{liter}$

Thus, capacity of the bowl $=\frac{303.1875}{1000}$

$=0.303\mathrm{lit}e\mathrm{rs}$ [ Approx.]

Hence, the hemispherical bowl can hold $0.303\mathrm{lit}e\mathrm{rs}$ of milk.