Question

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

Options

• 1 : 2

• 1 : 4

• 1 : 6

• 1 : 8

Answer 1

1 : 4

Explanation;

Hint:

Let the radius of the cylinder be "r" and the height be "h"

Radius of the new cylinder = `"r"/2` ...(Height will be same)

Volume of the new cylinder : Volume of the original cylinder

= `pi"r"_1^2"h" : pi"r"_2^2"h"`  ...(πh is same)

= `pi_1^2 : "r"_2^2`

= `("r"/2)^2 : "r"^2`

= `("r"^2)/4 : "r"^2 = 1/4 : 1`

= 1 : 4