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

(a) 1 : 2
(b) 2 : 1
(c) 1 : 4
(d) 4 : 1 [CBSE 2012]

Answer 1

Let the radius and height of the original cylinder be R and h, respectively.
Now, the radius of the new cylinder = $\frac{R}{2}$
Then, the ratio of the volume of the cylinder thus obtained to the volume of original cylinder is given by
$$\begin{gathered} \mathrm{\pi }{\left(\frac{R}{2}\right)}^{2}h:\mathrm{\pi }{R}^{2}h \\ =\frac{1}{4}:1 \\ =1:4 \end{gathered}$$

Hence, the correct answer is option C.