Question

Question 90

The radius and height of a cylinder are in the ratio 3 : 2 and its volume is $19404c{m}^3$. Find its radius and height.

Answer 1

The radius and height of a cylinder are in the ratio 3 : 2
Let the radius be 3x and height be 2x. Then,
Volume of cylinder $=19404c{m}^3$ [given]
$\because$ Volume of a cylinder $=\pi r^{2}h$
$\therefore$ $19404=\frac{22}{7}\times (3x{)}^2\times (2x)$
$\Rightarrow 19404=\frac{22}{7}\times 9x^2\times 2x=\frac{22\times 18x^3}{7}\Rightarrow 19404=\frac{396x^3}{7}\Rightarrow x^3=343\Rightarrow x^3=(7{)}^3\therefore x=7cm$
Hence, radius of the cylinder $=3\times 7=21cm$
and height of the cylinder $=2\times 7=14cm$