Question

If the radius of the base of a right circular cylinder is halved, keeping the height the same, then the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is:

Options

•  1 : 2

•  2 : 1

•  1 : 4

•  4 : 1

Answer 1

Let the radius and height of the original cylinder be r and h respectively.

∴Volume of the original cylinder = πr²h

According to the question, radius of the new cylinder is halved keeping the height same.

⇒ Radius of the new cylinder`=r/2`

Also, height of the new cylinder = h

∴ Volume of the new cylinder `pi(r/2)^2h=(pir^2h)/4`

`\text{Volume of the new cylinder}/\text{Volume of  original cylinder}=(((pir^2h)/4))/(r^2h4)=underline1=1:4`

Hence, the correct answer is C.