Question

What is the volume of the hemisphere bowl if its radius is 21m?
a.$19404{{m}^{3}}$
b.$1904{{m}^{3}}$
c.$19303{{m}^{3}}$
d.$19505{{m}^{3}}$

Answer 1

Hint: In the volume of hemisphere, substitute the radius of the given hemisphere bowl. Simplify the expression and get the volume of hemisphere in ${{m}^{3}}$.

Complete step-by-step answer:

We know that a hemisphere is a 3 – dimensional object that is half of a sphere. Volume is the amount of space inside of an object.

Thus the formula for the volume of hemisphere $=\dfrac{2\pi {{r}^{3}}}{3}$
We have been given the radius of the hemisphere as 21m.
Let us put radius r. Thus it means that, r = 21m.
Consider, $\pi =\dfrac{22}{7}$
Now let us apply these values in the volume of the hemisphere.
Volume of hemisphere $=\dfrac{2\pi {{r}^{3}}}{3}$
$\begin{aligned} & =\dfrac{2}{3}\times \dfrac{22}{7}\times {{\left( 21 \right)}^{3}} \\\ & =\dfrac{2}{3}\times \dfrac{22}{7}\times 21\times 21\times 21 \\\ \end{aligned}$
Cancel out the like terms and simplify it.
$\therefore$ Volume of hemisphere $=44\times 7\times 3\times 21$
$\begin{aligned} & =44\times 21\times 21 \\\ & =19404{{m}^{3}} \\\ \end{aligned}$
Thus we got the volume of the hemisphere bowl as $19404{{m}^{3}}$.
$\therefore$ Option (a) is the correct answer.

Note: If you need to find the area of the hemisphere, then use the formula, $2\pi {{r}^{2}}$, where r is the radius. This is the curved surface area.
The total surface area of the hemisphere will be the curved surface area and area of the base circle.
Total surface area = curved surface area + area of the base circle
= $2\pi {{r}^{2}}+\pi {{r}^{2}}=3\pi {{r}^{2}}$