Question

Choose the correct answer of the following 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 base radius and height of the original cylinder be r and h, respectively

Also,

The radius of the cylinder, `"R" = "r"/2` and its height, H = h.

Now,

The ratio of the volume of the new cylinder to that of the original cylinder`="Volume of the new cylinder"/"Volume of the original cylinder" ` 

`=(pi"r"^2"h")/(pi"R"^2"H")`

`=(pi"r"^2"h")/(pi("r"/2)^2"h")`

`= (4pi"r"^2"h")/(pi"r"^2"h")`

`=4/1`

= 4 : 1

Hence, the correct answer is option (d).