Question

A sphere is inserted in a cylindrical pipe such that the sphere is touching every surface of the cylinder. What is the ratio of the volume of the cylinder to the volume of the sphere?

• A. $6:5$
• B. $3:2$
• C. $2:3$
• D. $5:2$

Answer 1

The correct option is B $3:2$

The situation can be explained through the figure given below.



$\text{Radius of the sphere}=r$
$\text{Radius of the cylinder}=r$
$\text{Height of the cylinder}=2r$

$\text{Volume of a cylinder}=\pi r^{2}h$
$h\text{is the height}$.
$r\text{is the radius}$.

$\text{Volume of a cylinder}=\pi r^2\times 2r$
$=2\pi r^3$

$\text{Volume of a sphere}=\frac{4}{3}\pi r^3$
$r\text{is the radius}$.

So, ratio of volume of cylinder to the volume of sphere is
$2\pi r^3:\frac{4}{3}\pi r^3$

$\Rightarrow 2:\frac{4}{3}$

$\Rightarrow 6:4$

$=3:2$