Question

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.
b. Find its volume.​

Answer 1

Answer:

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

Answer 2

Answer :

The total surface area and volume of the cylinder is

Step-by-step explanation :

Given that,

• Length = 44 cm
• Breadth = 20 cm

Solution,

Breadth of rectangle = Height of the cylinder, therefore, height = 20 cm

Length of Rectangle = Circumference, therefore, circumference = 44 cm

44 cm = Circumference

» 44 = 2πr

» 44 = 2 × 22/7 × 44

» r = 44 × 7 / 44

» r = 7

Hence, radius of the cylinder is 7 cm.

• Total surface area

» 2πr( h + r )

» 2 × 22/7 × 7 × ( 20 + 7 )

» 2 × 22 × 27

» 44 × 27

» 1188 cm²

Hence, Total surface area of cylinder is 1188 cm²

• Volume of the cylinder

» πr²h

» 22/7 × ( 7 )² × 20

» 22/ 7 × 7 × 7 × 20

» 22 × 7 × 20

» 154 × 20

» 3080 cm³

Hence, the volume of the cylinder is 3030 cm³