Volume of a sphere of radius $\frac{r}{2}$ is equal to

Concept: The capacity of a sphere is measured by its volume. It's the area that the spherical takes up. Cubic units, such as m³, cm³, in³, and so on, are used to measure the volume of a sphere.

The sphere is round and three-dimensional in shape. It has three axes that define its shape: x-axis, y-axis, and z-axis. All items with volume, such as football and basketball, are instances of spheres.

Because the cross-section of the sphere is a circle, the volume here is determined by the diameter of the radius of the sphere.

Volume of Sphere is calculated using formula:

$\Rightarrow Volume of Sphere = \frac{4}{3}\pi r^3$

Given: r =  $\frac{r}{2}$

Therefore,

$\Rightarrow V = \frac{4}{3}\pi r^3$

$\Rightarrow \frac{4}{3}\pi {\left(\frac{r}{2}\right)}^3$

$\Rightarrow \frac{4}{3}\times \pi \times \frac{r^3}{8}$

$\Rightarrow \frac{1}{6}\pi r^3$

$\therefore V= \frac{\pi r^3}{6}$

Hence, the volume is $\frac{\pi r^3}{6}$.