Q. 52

A. 2 : 1

B. 3 : 1

C. 4 : 1

D. 5 : 1

Answer :

Given: Radius and height of the Cylinder are 80cm and 20cm respectively.

Lateral Surface area of a Cylinder is : 2πrh

Let S_{1} be the Lateral surface area of the Cylinder

∴ S_{1} = 2πrh

⇒ S_{1} = 2 × π × 80 × 20 = 3200π

Total Surface area of a Cylinder is : 2πr(r + h)

Let S_{2} be the Total surface area of the Cylinder

∴ S_{2} = 2πr(r + h)

⇒ S_{2} = 2 × π × 80 × (80 + 20) = 16000π

Ratio of Total surface area to Lateral surface area id S_{2} : S_{1}

∴ S_{2} : S_{1} = 16000π : 3200π

⇒ S_{2} : S_{1} = 5:1

∴ The ratio of the total surface area to the lateral surface area of a cylinder is 5:1

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