Question

In a cylinder, if radius is halved and height is doubled, the volume will be ______.

Options

• same

• doubled

• halved

•  four times

Answer 1

Let V₁ be the volume of the cylinder with radius r₁ and height h₁, then

 `V_1 = pir_1^2h_1`   ……. (1)

Now, let V₂ be the volume after changing the dimension, then

`r_2 = 1/2r_1 , h_2 = 2h_1`

So,

`V_2 = pir_2^2 h_2 = pi xx ((r_1)/2)^2 xx 2h_1`

`⇒ V_2 = 1/2 xx pi r_1^2 h_1 = 1/2V_1`