Question

The height of a right circular cylinder is 1.5 times the radius of the base. What is the ratio of the total surface area to the lateral (curved) surface area of the cylinder?

Answer 1

The ratio of the total surface area to the lateral (curved) surface area of the cylinder is 5:3

Explanation:

The height of a right circular cylinder is 1.5 times the radius of the base.

Let the radius of base be x

So, Height of a right circular cylinder = 1.5x

Total surface area of cylinder =
`2 \pi r h + 2 \pi r^2 = 2 \pi r(h+r)=2 \pi * x(x+1.5x)=2 \pi * x * 2.5x`

Curved surface area of cylinder =
`2 \pi rh = 2 \pi * x * 1.5 x`

So, Ratio of the total surface area to the lateral (curved) surface area of the cylinder =
`(2 \pi * x * 2.5x)/(2 \pi * x * 1.5 x)=(2.5)/(1.5)=(25)/(15)=(5)/(3)`

Hence the ratio of the total surface area to the lateral (curved) surface area of the cylinder is 5:3