Question

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Answer 1

Question:

A rectangular sheet of paper 44 cm × 14 cm is rolled along its length and a cylinder is formed. Find the volume of cylinder.

Given:

✰ A rectangular sheet is rolled along its length and a cylinder is formed.

✰ Length of a rectangular sheet of paper = 44 cm

✰ Breadth of a rectangular sheet of paper = 14 cm

To find:

✠ The volume of cylinder.

Solution:

Let's understand the concept first!

We know that the rectangular sheet of paper is rolled along its length and a cylinder is formed. So the breadth of the rectangular sheet of paper becomes the height of the cylinder formed, whereas the length of the the rectangular sheet of paper is the circumference of base of a cylinder. Using formula of circumference, we will find the radius of a cylinder and after that we will substitute the value of height and radius in the formula of volume of cylinder to calculate the volume of cylinder.

Let's find out...✧

⤳ Breadth of a rectangular sheet of paper = Height of a cylinder

⤳ Height of a cylinder = 14 cm

✭ Circumference of a cylinder = 2πr ✭

Where,

• r is the radius of a cylinder.

⤳ Length of a rectangular sheet of paper = Circumference of a cylinder

⤳ Circumference of a cylinder = 2πr

⤳ 2πr = 44

⤳ 2 × 22/7 × r = 44

⤳ 44/7 × r = 44

⤳ r = 44 × 7/44

⤳ r = 7 cm

∴ The radius of a cylinder = 7 cm

Now,

✭ Volume of a cylinder = πr²h ✭

Where,

• r is the radius of a cylinder.
• h is the height of a cylinder.

Putting the values in the formula, we have:

➤ Volume of a cylinder = 22/7 × 7 × 14

➤ Volume of a cylinder = 22 × 14

➤ Volume of a cylinder = 308 cm³

∴ The volume of a cylinder = 308 cm³

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