Question

the radii of two right circular cylinders are in ratio 2:3 and their height are in the ratio 5:4 . find the ratio of their curved surface area.

Answer 1

Step-by-step explanation:

$\bf{\underline{\underline\red{Given:-}}}$

• The radii of two right circular cylinders are in ratio 2 : 3

• The height s are in the ratio 5 : 4.

$\bf{\underline{\underline\blue{To\:Find:-}}}$

• The ratio of their curved surface area.

$\bf{\underline{\underline\green{Solution:-}}}$

Let the common ratio between the radii be r

$\rm Radius \: of \: first \: cylinder \: (r_{1})= 2r$

$\rm Radius \: of \: second \: cylinder \: (r_{2})= 3r$

Let the common ratio between the heights be h

$\rm Height \: of \: first \: cylinder \: (h_{1})= 5h$

$\rm Height \: of \: second \: cylinder \: (h_{2})=4h$

As we know that:-

Curved surface area (CSA ) of a cylinder is given by the formula:-

$\boxed{ \rm \leadsto CSA \: of \: cylinder \: = 2\pi rh}$

$\rm \implies CSA \: of \:first \: cylinder \: (S_{1}) = 2\pi r_{1} h_{1}......(i)$

$\rm \implies CSA \: of \: second\: cylinder \: (S_{2}) = 2\pi r_{2} h_{2}......(ii)$

Dividing (i) by (ii)

$\rm \implies \dfrac{ S_{1} }{ S_{2 }} = \dfrac{2\pi r_{1} h_{1}}{2\pi r_{2} h_{2}}$

$\rm \implies \dfrac{ S_{1} }{ S_{2 }} = \dfrac{2\pi \times 2r \times 5h}{2\pi \times 3r \times 4h}$

$\rm \implies \dfrac{ S_{1} }{ S_{2 }} = \dfrac{10}{12}$

$\rm \implies \dfrac{ S_{1} }{ S_{2 }} = \dfrac{5}{6}$

$\rm \implies S_{1}: S_{2} = 5 : 6$

Therefore:-

The ratio of the the curved surface area is 5 : 6

Answer 2

Given that ,

• The radii of two right circular cylinders are in ratio 2 : 3

• The height of two right circular cylinders are in the ratio 5 : 4

Let ,

The radii of two right circular cylinders be 2x and 3x

The height of two right circular cylinders be 5x and 4x

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

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

So , the ratio of CSA of given two right circular cylinders will be

$\tt \implies \frac{2 \pi \times 2x \times 5x}{2 \pi \times 3x \times 4x}$

$\tt \implies \frac{5}{6}$

The required ratio is 5 : 6