Question

4. A rectangular sheet of paper 44 cm x 20 cm is rolled along its length to make a cylinder. A circular sheet of paper is attached to the bottom of the cylinder formed. Find the capacity and total surface area of the cylinder so formed.​

Answer 1

Answer:

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Step-by-step explanation:

We know that the curved surface area of a right circular cylinder with radius r and height h is CSA=2πrh.

It is given that the length of the rectangular sheet is l=44 cm and the height of the sheet is h=20 cm. Since the cylinder is formed among the length, therefore, length of rectangular sheet is equal to circumference of base that is:

l=2πr

⇒44=2×

7

22

×r

⇒r=

2×22

44×7

=7

Therefore, the radius of the rectangular sheet is 7 cm.

We also know that the volume of a right circular cylinder with radius r and height h is V=πr

2

h.

Here, the height is h=20 cm and the radius is r=7 cm, therefore,

V=πr

2

h=

7

22

×(7)

2

×20=

7

22

×49×20=3080 cm

3

Answer 2

Given data :

➜ Length of rectangular sheet of paper = 44 cm

➜ Breadth of rectangular sheet of paper = 20 cm

Solution : Here, we know through question that, a rectangular sheet of paper is rolled along its length to make a cylinder. Hence, circumference of its bottom and top is 20 cm and height of cylinder is 44 cm.

Now,

➜ Circumference of bottom = 2πr

➜ 20 = 2πr

➜ r = 20/2π

➜ r = 10/π cm ----{1}

Now,

➜ Volume of cylinder = πr²h

➜ Volume of cylinder = π * (10/π)² * 44

➜ Volume of cylinder = π * (100/π²) * 44

➜ Volume of cylinder = (100/π) * 44

➜ Volume of cylinder = (44 * 100)/π

➜ Volume of cylinder = 4400/π

➜ Volume of cylinder = 4400/(22/7)

➜ Volume of cylinder = (4400/22) * 7

➜ Volume of cylinder = 200 * 7

➜ Volume of cylinder = 1400 cm³

∴ The capacity of the cylinder is 1400 cm³.

Now,

➜ Total surface area of cylinder = 2πr²h

➜ Total surface area of cylinder = 2π * (10/π)² * 44

➜ Total surface area of cylinder = 2π * (100/π²) * 44

➜ Total surface area of cylinder = (200/π) * 44

➜ Total surface area of cylinder = (44 * 200)/π

➜ Total surface area of cylinder = 8800/π

➜ Total surface area of cylinder = 8800/(22/7)

➜ Total surface area of cylinder = (8800/22) * 7

➜ Total surface area of cylinder = 400 * 7

➜ Total surface area of cylinder = 2800 cm²

∴ Total surface area of cylinder is 2800 cm³.

Answer : Hence, the capacity of the cylinder is 1400 cm³ and total surface area of the cylinder is 2800 cm³.