35.0k views
3 votes
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?

User Zammuuz
by
6.8k points

1 Answer

2 votes

Answer:

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

User Franz Forstmayr
by
7.0k points