Question

From a rectangular tin sheet, 110 cm long and 15 cm broad, a cylindrical pipe of height
15 cm is made. Find the diameter of the pipe.​

Answer 1

Given:

✰ Length of a rectangular sheet = 110 cm

✰ Breadth of a rectangular sheet = 15 cm

✰ Height of a cylindrical pipe = 15 cm

To find:

✠ The diameter of the pipe.

Solution:

Let's understand the concept first!

• As we are provided with the length and breadth of a rectangular sheet, so first we will find area of a rectangular sheet. Putting the values in the formula and then doing the required calculations.
• Then we know that the area of rectangular sheet is equal to the area of a cylindrical pipe and we have provided with the height of a cylindrical, so using formula of curved surface area of cylinder, we will find the radius of cylinder.
• After that by using radius, we will find the diameter of the cylindrical pipe.

✭ Area of a rectangle = l × b ✭

Here,

• l is the length of a rectangular sheet.
• b is the breadth of a rectangular sheet.

Putting the values in the formula, we have:

⤳ Area of a rectangular sheet = l × b

⤳ Area of a rectangular sheet = 110 × 15

⤳ Area of a rectangular sheet = 1650 cm²

∴ The Area of a rectangular sheet = 1650 cm²

Now,

Area of a rectangular sheet = Area a cylindrical pipe

∴ Area a cylindrical pipe = 1650 cm²

✭ Area of a cylinder = 2πrh ✭

Here,

• r is the radius of a cylindrical pipe.
• h is the height of a cylindrical pipe.

Putting the values in the formula, we have:

➛ 1650 = 2 × 22/7 × r × 15

➛ 1650 = 44/7 × r × 15

➛ 1650/15 = 44/7 × r

➛ 110 = 44/7 × r

➛ r = 110 × 7/44

➛ r = 10 × 7/4

➛ r = 2.5 × 7

➛ r = 17.5 cm

∴ The radius of cylindrical pipe = 17.5 cm

Then,

✭ Diameter = 2 × radius ✭

Putting the values in the formula, we have:

⤳ Diameter = 2 × 17.5

⤳ Diameter = 35 cm

∴ The diameter of a cylindrical pipe = 35 cm

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