Question

The curved surface area and the total surface area of a right circular cylinder are in the ratio 5:9. Find the ratio between its height and radius. ​

Answer 1

Answer:

The answer is 5 : 4.

Step-by-step explanation:

Let , the length of the radius and the length of the height of a right circular cylinder are r and h respectively.

Then , The curved surface area of the cylinder is 2πrh square units.

The total surface area of a cylinder is ( 2πrh + 2πr² ) = 2πr( h + r ) square units.

According to the question ,

2πrh/2πr( h + r ) = 5/9

⇒ h/( h + r ) = 5/9

⇒ ( h + r )/h = 9/5

⇒ 1 + r/h = 9/5

⇒ r/h = 4/5 ⇒ h/r = 5/4