Question

27. Two right circular solid cylinders have radii in
the ratio 3 : 5 and heights in the ratio
2: 3. Find the ratio between their :
(i) curved surface areas.
(ii) volumes.​

Answer 1

Answer:

(i) Ratio of their curved surface areas is 2:5.

(ii) Ratio of their volumes is 6:25.

Step-by-step explanation:

Given :-

• Two right circular solid cylinders have radii in the ratio 3:5 and heights in the ratio 2:3.

To find :-

• Ratio between their (i) curved surface areas and (ii) volumes.

Solution :-

Consider,

• Radii of 1st cylinder = 3x units
• Radii of 2nd cylinder = 5x units

And,

• Height of 1st cylinder = 2y units
• Height of 2nd cylinder = 3y units

Formula Used :

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

Then,

★CSA of 1st cylinder,

= [2 × (22/7) × 3x × 2y ] Unit ²

= 264xy/7 unit²

★ CSA of 2nd cylinder,

= [2 × (22/7) × 5x × 3y ] Unit ²

= 660xy/7 unit²

Ratio of their curved surface areas,

= 1 st cylinder : 2nd cylinder

= 264xy/7 : 660xy/7

= 2:5

Therefore, the ratio of their curved surface areas is 2:5.

Formula used :

${\boxed{\sf{Volume\:of\: cylinder=\pi\:r^2h}}}$

Then,

★Volume of 1st cylinder,

= [π × 3x × 3x × 2y ] unit³

= 18πx²y unit³

★ Volume of 2nd cylinder,

= [π × 5x × 5x × 3y] unit³

= 75πx²y unit³

Ratio of their volumes,

18πx²y : 75πx²y

= 6 : 25

Therefore, the ratio of their volumes is 6:25.