Question

A rectangular sheet of paper 30 cm into 18 cm can be transformed into the curved surface of a right circular cylinder interviews namely either by Rolling the paper along its length or ride along its base find the ratio of its volume of the two cylinders thus formed

Answer 1

Answer:

5:3

Step-by-step explanation:

Given dimensions are 30cm * 18cm.

(i)

Let v₁ be the volume of cylinder which is formed by rolling the sheet along its length.

Given, height(h₁) = 18 cm.

We know that circumference of base of cylinder = 2πr₁ = 30

⇒ πr₁ = 15

⇒ r₁ = 15/π

We know that volume of cylinder(v₁) = πr²h

⇒ πr₁²h₁

⇒ π(15/π)(15/π) * 18

⇒ (4050/π) cm³

(ii)

Let v₂ be the volume of cylinder which is formed by rolling the sheet along its width.

Given, height(h₂) = 30 cm.

We know that circumference = (2πr₂)

⇒ 2πr₂ = 18

⇒ πr₂ = 9

⇒ r₂ = (9/π)

We know that volume of cylinder(v₂) = πr²h

⇒ πr₂²h₂

⇒ π(9/π)(9/π)*(30)

⇒ (2430/π) cm³

Now,

v₁ : v₂

⇒ (4050/π) : (2430/π)

⇒ 4050:2430

⇒ 5:3.

Therefore, ratio of volume of the volume of two cylinders formed = 5:3

Hope it helps!