Question

The radius of a sphere is 2r, then the volume will be:
A. ${\displaystyle \frac{4}{3}}\pi r^3$
B. $4\pi r^3$
C. ${\displaystyle \frac{8\pi r^3}{3}}$
D. ${\displaystyle \frac{32}{3}}\pi r^3$

Answer 1

Hint: We have been given the radius of the sphere as ‘2r’. We know that the volume of the cube is given by the formula ${\displaystyle \frac{4}{3}}\pi R^3$ where ‘R’ is the radius of the sphere. Thus, we will put the value of the given radius in this formula and hence, we will obtain the value of the required volume.

Complete step by step answer:
Now, we have been given that the radius of the sphere is ‘2r’.

We know that the volume of a sphere with radius ‘R’ is given by the formula:
$Volume={\displaystyle \frac{4}{3}}\pi R^3$
Here $R=2r$
Thus, we can obtain the volume of the cube by putting the value of ‘R’ in the formula of the volume of a sphere mentioned above.
Thus, putting the value of ‘R’ in the formula we get:
$\begin{array}{rl}& Volume={\displaystyle \frac{4}{3}}\pi {\left(2r\right)}^3\\ & \Rightarrow Volume={\displaystyle \frac{4}{3}}\pi \left(8r^3\right)\\ & \Rightarrow Volume={\displaystyle \frac{32}{3}}\pi r^3\end{array}$
Therefore, the required volume of the sphere is ${\displaystyle \frac{32}{3}}\pi r^3$
Hence, option (D) is the correct option.

Note:
Be careful with the formula for the volume of the sphere. It is easy to confuse it with the formula for the volume of a hemisphere. Volume of a hemisphere is given by the formula ${\displaystyle \frac{2}{3}}\pi R^3$ where ‘R’ is the radius of the hemisphere. We can remember it by the fact that a hemisphere is like a half sphere and so is its volume (volume of a sphere with a radius ‘R’ is given by ${\displaystyle \frac{4}{3}}\pi R^3$ ).