Question

The radil of two cylinders are in the ratio 2:3 and their heights are in the ratio
5:3. Calculate the ratio of their curved surface areas.​

Answer 1

Answer :

➥ The ratio of their curved surface areas = 10:9

Given :

➤ Radii of two cylinders = 2:3

➤ Height of two cylinders = 5:3

To Find :

➤ Ratio of their curved surface areas = ?

Solution :

Let ,

The radius of cylinder be "r₁" and "r₂" and the height of the cylinder be "h₁" and "h₂"

As we know that

Curved surface area of cylinder = 2πrh

$\tt{\longmapsto \dfrac{r_{1}}{r_{2}} = \dfrac{2}{3} }$

$\tt{\longmapsto \dfrac{h_{1}}{h_{2}} = \dfrac{5}{3} }$

Now ,

The ratio of their curved surface areas

$\tt{: \implies \dfrac{\cancel{2\pi} r_1 h_1 }{\cancel{2\pi} r_2 h_2 } }$

$\tt{:\implies\dfrac{r_{1}}{r_{2}} \times \dfrac{h_{1}}{h_{2}} }$

$\tt{: \implies \dfrac{2}{3} \times \dfrac{5}{3} }$

$\tt{: \implies \dfrac{10}{9} }$

$\bf{: \implies \underline{\:\:{\underline{\purple{\:\:{ 10:9\:\:}}}} \: \: }}$

Hence, the ratio of their curved surface areas is 10:9.

Answer 2

Given ,

The radil of two cylinders are in the ratio 2 : 3 and their heights are in the ratio 5 : 3

Let ,

The radii of two cylinder be 2x and 3x

The height of two cylinder be 5x and 3x

We know that , the curved surface area of cylinder is given by

$\boxed{ \tt{CSA = 2\pi rh}}$

Thus ,

The ratio of two given cylinder will be :

$\implies \tt \frac{2\pi \times 2x \times 5x}{2\pi \times 3x \times 3x}$

$\implies \tt \frac{2x \times 5x}{3x \times 3x}$

$\implies \tt \frac{10x}{9x}$

$\implies \tt \frac{10}{9}$