Question

a rectangular sheet of paper 35cm×21cm can be transformed into the curved surface of a right cicular cylinder in two ways i.e, either by rolling the paper along its length or along its breadth find the ratio of the volume of the two cylinder thus formed​

Answer 1

Answer:

682.38 cm³ (approx) when rolled along its length

409.43 cm³ (approx) when rolled along its width

Step-by-step explanation:

Rolling along its length, the cylinder has height 21 cm and circumference (of its base) equal to 35 cm.

Let r be the radius.

Circumference = 2 π r = 35  =>  r = 35 / 2π

Area of base = π r² = π × 35² / 4π² = 1225 / 4π

Volume of cylinder = (1/3) × (area of base) × (height)

= (1/3) × (1225/4π) × 21

≈ 682.38 cm³ (approx)

Rolling the other way, height = 35cm and circumference = 21cm.

Let r be the radius.

Circumference = 2 π r = 21  =>  r = 21 / 2π

Area of base = π r² = π × 21² / 4π² = 441 / 4π

Volume of cylinder = (1/3) × (area of base) × (height)

= (1/3) × (441/4π) × 35

≈ 409.43 cm³ (approx)