A rectangular piece of paper 11cm × 4cm is folded without overlapping to make a cylinder of height 4cm. Find the volume of the cylinder.

Let's understand how a rectangular sheet of paper can be converted in to a cylinder.

Answer: The volume of a cylinder with height as 4cm which is to be made of a rectangular piece of paper with dimensions 11 cm × 4 cm is 38.5 cm³

Let's find the volume of the cylinder.

Explanation:

Given : The dimensions of the rectangular paper is 11cm × 4cm

Height of the cylinder is 4cm

Let's look into the below diagram to understand how a rectangular sheet of paper can be converted in to a cylinder

The length of the paper 'l' becomes the circumference of the base of the cylinder and breadth 'b' becomes height of the cylinder

Let the radius of the base and height of the cylinder be 'r' and 'h' respectively

Circumference of the base of cylinder = Length of the rectangle

=> 2πr = 11

=> 2× 22/7 × r = 11

=> r = 7/4 cm

Height of the cylinder = 4cm (given)

Volume of the cylinder is πr²h

Substituting the values of 'r' and 'h' we get

=> (22 × 7 × 7 × 4) / (7 × 4 × 4)

=> 38.5 cm³

Thus, the volume of a cylinder with height as 4cm which is to be made of a rectangular piece of paper with dimesions 11 cm × 4 cm is 38.5 cm³