The ratio of the total surface area to the lateral surface area of a cylinder with base radius 80 cm and height 20 cm is
Given: Radius and height of the Cylinder are 80cm and 20cm respectively.
Lateral Surface area of a Cylinder is : 2πrh
Let S1 be the Lateral surface area of the Cylinder
∴ S1 = 2πrh
⇒ S1 = 2 × π × 80 × 20 = 3200π
Total Surface area of a Cylinder is : 2πr(r + h)
Let S2 be the Total surface area of the Cylinder
∴ S2 = 2πr(r + h)
⇒ S2 = 2 × π × 80 × (80 + 20) = 16000π
Ratio of Total surface area to Lateral surface area id S2 : S1
∴ S2 : S1 = 16000π : 3200π
⇒ S2 : S1 = 5:1
∴ The ratio of the total surface area to the lateral surface area of a cylinder is 5:1