Question

The radii of 2 cylinders are in the ratio 2:3 and their heights are in the ratio 5:3. Calculate the ratio of their curved surfaces.​

Answer 1

Answer:

Ratio of their curved surfaces is 10:9

Step-by-step explanation:

Curved surface of the cylinder is 2πrh

Curved surface for first cylinder is 2π x 2 x 5 = 20π

Curved surface for second cylinder is 2π x 3 x 3 = 18π

Ratio of their curved surfaces. is = 20 π : 18 π = 10: 9

Hence the ratio is 10: 9

Answer 2

Answer:

The ratio of their curved surface is 10 : 9    

Step-by-step explanation:

Given as :

The radius of two cylinder are in ratio 2 : 3

i. radius are 2 x  , 3 x

The height of two cylinder are in ratio 5 : 3

i.e height are 5 y  , 3 y

Since curved surface area of cylinder = 2 × π × r × h

where r is radius

and h is height

So, the ratio of curved surface area

$\dfrac{curved surface of cylinder _1}{curved surface of cylinder _2}$  = $\dfrac{2 \pi r_1 h_1}{2 \pi r_2 h_2 }$

i.e $\dfrac{curved surface of cylinder _1}{curved surface of cylinder _2}$ = $\dfrac{2 \Pi \times 2 x \times 5 y}{2 \times \Pi \times 3 x\times 3 y}$

Or, $\dfrac{curved surface of cylinder _1}{curved surface of cylinder _2}$ = $\dfrac{10}{9}$

So, the ratio of $\dfrac{curved surface of cylinder _1}{curved surface of cylinder _2}$ = $\dfrac{10}{9}$

Hence, The ratio of their curved surface is 10 : 9       Answer