Question

If the radius of a cylinder is r and the height is h, how will the volume change, if the (i) height is doubled, (ii) height is doubled and the radius is halved and (iii) height is same and the radius is halved?

Answer 1

Answer : -

(i) $\pi r^2 2h$units

(ii) $\pi h$ units

(iii) $\pi {\frac{h}{2}}$ units

Step-by-step explanation : -

Given that,

Height = h

Radius = r

(i) Height is doubled.

Let height be considered as 2h.

We know that,

Volume of a cylinder = $\pi r^2 h$

[By substituting the values],

Volume of the cylinder = $\pi r^2 2h$

Therefore, the volume of the cylinder will be $\pi r^2 2h$units, when height is doubled.



(ii) Height is doubled and the radius is halved.

(ii) Height is doubled and the radius is halved.

Here, the radius is $\frac{1}{2}$ and height is 2h.

Volume of a cylinder = $\pi r^2 h$

[By substituting the values],

Volume of the cylinder = $\pi {\frac{1}{2}} 2h$

Volume of the cylinder = $\pi \frac{1}{\cancel{2}} \cancel{2}h$

Volume of the cylinder = $\pi \times 1 \times h$

Volume of the cylinder = $\pi \times h$

Volume of the cylinder = $\pi h$

Therefore, the volume of the cylinder will be $\pi h$ units, when the height is doubled and the radius is halved.

(iii) Height is same and the radius is halved.

Here, the height is h and radius is $\frac{1}{2}$

Volume of a cylinder = $\pi r^2 h$

[By substituting the values],

Volume of the cylinder = $\pi {\frac{1}{2}} h$

Volume of the cylinder = $\pi {\frac{h}{2}}$

Therefore, the volume of the cylinder will be $\pi {\frac{h}{2}}$ units, when the height remains same and radius is halved.