Question

A cylinder is having a volume of 231 cu. cm. If the height of the cylinder is 6 cm, then what is the radius of a ball which will fit inside the cylinder?

• A. Circle
• B. 4 cm
• C. 2.5 cm
• D. 5 cm

Answer 1

Answer: (A), (C)

The correct options are
A

Circle

C

2.5 cm

Let the radius of the cylinder and ball be $r_c$ and $r_b$ respectively.

Given, height of the cylinder,$h=6cm$

Volume of the cylinder $=\pi \times {r_c}^2\times h=231c{m}^3$

$\Rightarrow \frac{22}{7}\times {r_c}^2\times 6=231$

$\Rightarrow {r_c}^2=231\times \frac{7}{22}\times \frac{1}{6}$

$\Rightarrow r_c=3.5cm$

So in order to fit a ball inside the cylinder,

Radius of the ball $⩽$ Radius of the Cylinder

$\Rightarrow r_b⩽r_c$

$\Rightarrow r_b⩽3.5cm$
So, the ball will fit inside the cylinder if its radius is less than 3.5 cm.
Hence 2.5 cm and 3 cm are the right options.