Question

A sphere,a cylinder and a cone are of same radius and same height and same radius. the ratio of their curved areas is

Answer 1

1:3 is there curved areas

Answer 2

Answer:

• Ratio is 4 : 4 : √5

Step-by-step explanation:

Given

• A sphere, a cylinder and a cone are of same radius and same height.

To find

• Ratio of their curved surface areas.

Solution

Let r be the common radius of a sphere, a cone and cylinder.

Then, height of sphere = its diameter = 2r

Then, height of cone = height of cylinder = height of sphere = 2r

Then, slant height of cone (l) = √r² + h²

• √r² + (2r)² = √r + 4r = √5r

S₁ = Curved surface area of sphere:

• 4πr²

S₂ = Curved surface area of cylinder:

• 2πrh = 2πr × 2r = 4πr²

S₃ = Curved surface area of cone:

• πrl = πr × √5r = √5πr²

∴ Ratio of curved surface area is:

S₁ : S₂ : S₃ = 4πr² : 4πr² : √5πr²

• 4 : 4 : √5

Hence, the ratio is 4 : 4 : √5