Question:
The volume of a right circular cylinder with its height equal to the radius is $25 \frac{1}{7} \mathrm{~cm}^{3}$. Find the height of the cylinder.
Solution:
We have,
Height $=$ Base radius i. e. $h=r$
As,
Volume of the cylinder $=25 \frac{1}{7} \mathrm{~cm}^{3}$
$\Rightarrow \pi r^{2} h=\frac{176}{7}$
$\Rightarrow \frac{22}{7} \times h^{2} \times h=\frac{176}{7}$
$\Rightarrow h^{3}=\frac{176 \times 7}{7 \times 22}$
$\Rightarrow h^{3}=8$
$\Rightarrow h=\sqrt[3]{8}$
$\therefore h=2 \mathrm{~cm}$
So, the height of the cylinder is 2 cm.