The base area and the curved surface area of a cylinder are equal. What is the ratio of the base radius and height?

Question

Philoid · Accepted Answer

Given: base area and the curved surface area of a cylinder are equal

r = radius of the cylinder

h = height of the cylinder

to find :

ratio of the base radius and height=?

Procedure :

We know that,

Curved surface area =perimeter of base of cylinder × height of cylinder

⇒Curved surface area = (2∏r)× h

Now, as,

base area and the curved surface area of a cylinder are equal

,we have

⇒∏r²=(2∏r)×h

⇒r = 2h

⇒ =

∴ ratio of the base radius and height is 2:1 i.e. r:h