Question

The curved surface area of a cylinder is 1320 cm² and its base had diameter 21 cm. Find the height and the volume of the cylinder.
[Use π = 22/7]

Answer 1

$\textbf{Given:}$

$\text{Base diameter of the cylinder=21 cm}$

$\text{Then, its radius r= \frac{21}{2} cm}$

$\text{Also,}$

$\text{Curved surface area of the cylinder= 1320 cm^2 }$

$\implies\;2\,\pi\,r\,h=1320$

$\implies\;2(\frac{22}{7})(\frac{21}{2})\,h=1320$

$\implies\;(\frac{22}{1})(\frac{3}{1})\,h=1320$

$\implies\;h=\frac{1320}{22{\times}3}$

$\implies\;h=\frac{440}{22}$

$\implies\boxed{\textbf{Height of the cylinder, h=20 cm}}$

$\textbf{Volume of the cylinder}$

$=\pi\,r^2\,h$

$=\frac{22}{7}{\times}\frac{21}{2}{\times}\frac{21}{2}{\times}20$

$=\frac{11}{1}{\times}\frac{3}{1}{\times}\frac{21}{1}{\times}10$

$=11{\times}3{\times}21{\times}10$

$=33{\times}210$

$=6930\;cm^3$

$\therefore\textbf{Volume of the cylinder=6930}\;cm^3$

Answer 2

The Height of the cylinder is equal to 20 cm

The Volume of the cylinder is equal to 6930 cm³

Let the height of the cylinder be h.

The radius of the cylinder = r = 21/2 = 10.5 cm

Given that the curved surface area of the cylinder = 2πrh = 1320 cm²

Solving to find the height -

=> 1320 = 2 × 22/7 × 10.5 × h

=> 660 = 22/7 × 10.5 × h

=> h = 20 cm

Height of the cylinder = 20 cm

The volume of the cylinder = πr²h

= 22/7 × (10.5)² × 20

= 6930 cm³