Question

The ratio between the curved surface area
and the total surface area of a cylinder is
1:2. Find the ratio between the height and the
radius of the cylinder​

Answer 1

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We know:-

• TSA of a cylinder = 2πr(r + h)
• CSA of the cylinder = 2πrh
• Ratio of CSA = 1 : 2

To FinD:-

• Ratio between the height and the radius of the cylinder

Then,

According to question,

⇒ CSA / TSA = 1 / 2

⇒ 2πrh / 2πr(r + h) = 1/2

⇒ h / r + h = 1/2

⇒ r + h = 2h

⇒ r = h

The required ratio:

Ratio between the height and the radius of the cylinder = 1 : 1

Answer 2

Required Answer:-

We know:-

• TSA of a cylinder = 2πr(r + h)
• CSA of the cylinder = 2πrh
• Ratio of CSA = 1 : 2

To FinD:-

• Ratio between the height and the radius of the cylinder

Then,

According to question,

⇒ CSA / TSA = 1 / 2

⇒ 2πrh / 2πr(r + h) = 1/2

⇒ h / r + h = 1/2

⇒ r + h = 2h

⇒ r = h

The required ratio:

Ratio between the height and the radius of the cylinder = 1 : 1