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A new cylinder is formed from previous cylinder in which radius is increased by 12.5% and height is increased by 37.5%. What is the ratio of curved surface area of old cylinder to the curved surface area of new cylinder?

A new cylinder is formed from previous cylinder in which radius is increased by 12.5% and height is increased by 37.5%. What is the ratio of curved surface area of old cylinder to the curved surface area of new cylinder? Correct Answer 64 : 99

Given:

Percentage increase in radius = 12.5%

Percentage increase in height = 37.5%

Formula Used:

CSA of cylinder = 2πrh

where, r → Radius of base, h → Height of cylinder, CSA → Curved Surface Area of cylinder.

Calculations:

Let the old height and new height be h1 and h2 respectively.

Let the old radius and new radius be r1 and r2 respectively.

Percentage increase in radius = 12.5%

⇒ r2 = r1 × (1 + 12.5/100)

⇒ r2/r1 = 9/8      ----(1)

Percentage increase in height = 37.5%

⇒ h2 = h1 × (1 + 37.5/100)

⇒ h2/h1 = 11/8      ----(2)

Now, CSA of old  cylinder/CSA of new  cylinder = 2πr1h1/2πr2h2

⇒ CSA of old  cylinder/CSA of new  cylinder = (r1/r2) × (h1/h2)

From (1) and (2), we get

⇒ CSA of old  cylinder/CSA of new  cylinder = 8/9 × 8/11 = 64/99

⇒ CSA of old  cylinder : CSA of new  cylinder = 64 : 99

∴ The ratio of curved surface area of old cylinder to the curved surface area of new cylinder is 64 : 99.

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