Question

If the radii of two cylinders are same and the height of one cylinder is double the height of the
other cylinder, then the ratio of their volume is

Answer 1

Given :-

• The radii of 2 cylinders are the same
• The height of one cylinder is double the height of the other cylinder.

Aim :-

• To find the ratio of the 2 cylinder's volume.

Let the radii of the cylinders take a value of 'r'.

Assuming the height of cylinder 2 to be 'h',

The height of cylinder 1 = 2h

Formula to use :-

Volume of a cylinder = πr²h

• r representing radius
• h representing height

Volume of cylinder 1 :-

Measurements :

• Radius = r
• Height = 2h

Substituting

Hence Volume :-

=≥ π × r² × 2h

=≥ 2πr²h

Volume of cylinder 2 :-

Measurements :

• Radius = r
• Height = h

Substituting,

Volume :-

=≥ π × r² × h

=≥ πr²h

Ratio :-

Ratio is the relation between any two or more quantities (or) the comparison between any two or more quantities in their simplest form.

The ratio of Cylinder 1 to Cylinder 2 :-

$\dfrac{2\pi {r}^{2} h}{\pi {r}^{2}h }$

Notice that πr²h is common in both.

Therefore cancelling them out we get :-

$\dfrac{2}{1}$

Hence the ratio of the 2 cylinder's volume :- 2 : 1 (C1 : C2)

Some more formulas :-

Total surface area of a cylinder = 2πrh + 2πr² =≥ 2πr(h+r)

Lateral surface area of a cylinder = 2πrh