If the radius of the base of a right circular cylinder is halved, keep

1.	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 isA) 2 : 1 B) 1 : 2 C) 4 : 1 D) 1 : 4
Answer» 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. Correct option is: C) 4 : 1

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 isA) 2 : 1 B) 1 : 2 C) 4 : 1 D) 1 : 4

Answer»

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.

Correct option is: C) 4 : 1