Question

20. A rectangular sheet of paper 44 cm long and 20 cm broad is rolled along its
length to form a cylinder.
a. Find its total surface area.
​

Answer 1

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

Hence, the volume of the cylinder is 3080 cm