Question

The volume of a solid hemisphere of radius 2 cm is?
(a) $\dfrac{352}{21}\text{ c}{{\text{m}}^{3}}$
(b) $576\text{ c}{{m}^{3}}$
(c) $\dfrac{376}{9}\ c{{m}^{3}}$
(d) $600\ c{{m}^{3}}$

Answer 1

Hint: Apply the formula for total volume of the hemisphere. Total volume of the hemisphere is equal to half of the volume of a sphere. Assume the radius of the sphere as ‘$r$’ and use the formula for volume of hemisphere $=\dfrac{2\pi {{r}^{3}}}{3}$.

Complete step-by-step answer:
A solid hemisphere is obtained when we cut a solid sphere into two equal halves. The volume of the hemisphere is half of the volume of the sphere. The prefix ‘hemi’ means half. So, a hemisphere is a three-dimensional shape that is half of a sphere with one flat circular side which is also known as the face of the hemisphere. In the real world, we will find hemispheres all around us. There are three types of hemisphere. First one is a hollow hemisphere which has only a lateral surface. Second one is a solid hemisphere that has a circular base in addition to the lateral surface. Last but not the least, the third one is a hemispherical shell defined as the solid enclosed between two concentric hemispheres.
Now let us come to the question.
We know that the volume of the hemisphere is $\dfrac{2\pi {{r}^{3}}}{3}$.
We have been given, $r=2\text{ cm}$. Therefore, volume of the given hemisphere
$\begin{align}
  & =\dfrac{2}{3}\times \dfrac{22}{7}\times {{2}^{3}} \\
 & =\dfrac{352}{21}\text{ c}{{\text{m}}^{3}} \\
\end{align}$
Hence, the volume of the given solid hemisphere is $\dfrac{352}{21}\text{ c}{{\text{m}}^{3}}$.
Therefore, option (a) is the correct answer.

Note: We have used the value of $\pi $ equal to $\dfrac{22}{7}$ because the options provided in the question are in fraction. We have to be careful about the unit of volume, that is ‘$c{{m}^{3}}$’. If the radius provided would have been in meters then the unit would have been ‘${{m}^{3}}$’. Never write the unit of volume as $c{{m}^{2}}\text{ or }{{m}^{2}}$ in a hurry because it is the unit of area.