Question

The heights of two cylinders are in the ratio 5:3 and their radii are in the ratio 2:3. Then, find the ratio of their curved surface area.​

Answer 1

CSA of First cylinder = 2 ( pi ) × r × h

= 2 × pi × ( 2x ) × ( 5x )

= 20 x² × pi

CSA of Second Cylinder = 2 ( pi ) × r × h

= 2 × ( pi ) × ( 3x ) × ( 3x )

= 18 x² × pi

Ratio of CSA = ( 20 x² × pi ) / ( 18 x² × pi )

= 20 : 18

= 10 : 9

Hence , ratio of their CSA is 10:9

Answer 2

Step-by-step explanation:

Curved Surface Area (CSA) of cylinder is given by

πr^2h

Where r is radius, h is height.

Given are two cylinders with radii 2:3

Let radii of both are 2x and 3x

Also, given are heights as 5:3

Let heights are 5y:3y

CSA of first cylinder (CSA1) = π2x^2.5y

( point . denotes multiplication)

CSA2 = π3x^2.3y

CSA1 : CSA2 = CSA1 / CSA2 = ( π2x^2.5y )/( π3x^2.3y )

= 2×5/3×3 = 10/9

So ratio of their CSA is 10:9