Question

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

A) 2 : 1 

B) 1 : 2 

C) 4 : 1 

D) 1 : 4

Answer 1

Correct option is: C) 4 : 1

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

\(\therefore\) Volume of original cylinder is \(V_1 = \pi r^2 h\)

When the radius of base of cylinder is halved and height remaining same, then, the volume of formed cylinder is

\(V_2 = \pi (\frac r2)^2h = \frac {\pi r^2h}{4}\)

Now, \(\frac {V_1}{V_2}\) = \(\frac {\pi r^2h}{\frac {\pi r^2h}4}\) = \(\frac 41 = 4:1\)

Hence, the ratio of the volume of cylinder thus obtained to the volume of the original cylinder is 4 :1.

Answer 2

Correct option is: C) 4 : 1