Question

Radii of hemispheres are given below. Arrange them according to the increasing order of their volume.

• A. $\frac{23}{4}$
• B. $\frac{11}{2}$
• C. $9$
• D. $\frac{17}{2}$
• E. 13

Answer 1

Let r be the radius of the sphere.
Volume of a hemisphere = $\frac{2}{3}\pi r^3$

Here, $\frac{2}{3}\pi$ is constant and the only variable is r.

As the value of r increases, $r^3$ increases and hence the volume of the hemisphere increases.
Here,
$\frac{17}{2}=8.5$
$\frac{23}{4}=5.75$
$\frac{11}{2}=5.5$

$\Rightarrow$ $\frac{11}{2}<\frac{23}{4}<\frac{17}{2}<9<13$

$\therefore$ The required order of radii will be:
$\frac{11}{2}$ < $\frac{23}{4}$ < $\frac{17}{2}$ < 9 < 13