Question

The radius of two right circular cylinder are in the ratio of 2 : 3 and their heights are in the ratio of 5: 4 calculate the ratio of their curved surface areas and also the ratio of their volumes.

Answer 1

Let the radii of two cylinders be 2r and 3r respectively and their heights be 5h and 4h respectively.
Let S₁ and S₂ be Curved Surface Area of the two cylinders and V₁ and V₂ be their volumes.

Then, S₁ = Curved surface area of the cylinders of height 5h and radius 2r.
⇒ 2π x 2r x 5h = 20πrh sq. units.

S₂ = Curved surface area of the cylinders of height 4h and radius 3r.
⇒ 2π x 3r x 4h = 24πrh sq. units.

`S_1/S_2 = (20πrh)/(24πrh) = 5/6`

S₁: S₂ = 5: 6

V₁ = Volume of cylinder of height 5h and radius 2r
= π x (2r)² x 5h = 20πr²h cubic units.

V₂ = Volume of the cylinder of height 4h and radius 3r.
= π x (3r)² x 4h = 36πr²h cubic units.

∴ `V_1/V_2 = (20πr^2h)/(36πr^2h) = 5/6`

V₁: V₂ = 5: 9.