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 \[=\dfrac{2\pi {{r}^{3}}}{3}\]
                                          \[\begin{align}
  & =\dfrac{2}{3}\times \dfrac{22}{7}\times {{\left( 21 \right)}^{3}} \\
 & =\dfrac{2}{3}\times \dfrac{22}{7}\times 21\times 21\times 21 \\
\end{align}\]
Cancel out the like terms and simplify it.
\[\therefore \] Volume of hemisphere \[=44\times 7\times 3\times 21\]
                                              \[\begin{align}
  & =44\times 21\times 21 \\
 & =19404{{m}^{3}} \\
\end{align}\]
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
                                 = \[2\pi {{r}^{2}}+\pi {{r}^{2}}=3\pi {{r}^{2}}\]