Question

The radius of a cylinder is doubled and the hieght remains the same. The ratio between the volumes of the new cylinder and the orignal cylinder is
a) 1:2
b) 3:1
c) 4:1
d) 1:8​

Answer 1

Given:-

• The radius of a cylinder is doubled
• height remains the same

To Find:-

• The ratio between the volumes of the new cylinder and the original cylinder.

Solution:-

Let the radius of original cylinder be r and height be h.

For original cylinder,

• Radius = r
• Height = h

We know,

• Curved Surface Area of the cylinder = 2πrh.

Hence,

CSA of original cylinder = 2πrh.

For new cylinder,

radius is doubled.

Hence,

• Radius = 2r
• Height = h

Curved Surface Area of the new cylinder is as follows:-

CSA = 2π × 2rh

⇒ CSA = 4πrh

Now,

Ratio between the Curved Surface Area of original cylinder and the new cylinder is as follows:-

• Ratio = CSA of original cylinder : CSA of new cylinder

⇒ Ratio = 2πrh : 4πrh

Here πrh cancels out for both numerator and denominator

Hence,

Ratio = 2 : 4

⇒ Ratio = 1 : 2

∴ Ratio between the Curved Surface Area of original cylinder and the new cylinder us 1 : 2

Hence, Option (a) 1 : 2 is the correct answer.

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Other formulas related to cylinder:

• Volume of cylinder = πr²h cu.units

• Total Surface Area = 2πr(r + h) sq.units

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