Question

The radius and height of a cylinder are in the ratio 3 : 2 and its volume is $19,404c{m}^3$. Find its radius and height.

• A. Radius = 14 cm
• B. Height = 14 cm
• C. Radius = 21 cm
• D. Height = 21 cm

Answer 1

Answer: (B), (C)

The correct options are
B Height = 14 cm
C Radius = 21 cm

The radius and height of a cylinder are in the ratio = 3 : 2
Let radius = 3x cm and height = 2x cm
Volume $=19,404c{m}^3$

Volume (V) = $\pi r^{2}h=19,404c{m}^3$
$\Rightarrow \frac{22}{7}\times (3x{)}^2\times 2x=19,404c{m}^3$
$\Rightarrow \frac{22}{7}\times 9x^2\times 2x=19,404c{m}^3$
$\Rightarrow \frac{22}{7}\times 18x^3=19,404c{m}^3$
$\Rightarrow x^3=\frac{19,404\times 7}{22\times 18}$
$\Rightarrow x^3=343c{m}^3$
$x=\sqrt[3]{3343}=7cm$
$\therefore$ Radius (r) = 3x
$=3\times 7=21cm$ and
Height (h)$=2x=2\times 7=14cm$