## Maharashtra State Board Class 8 Maths Solutions Chapter 16 Surface Area and Volume Practice Set 16.2

Question 1.

In each example given below, radius of base of a cylinder and its height are given. Then find the curved surface area and total surface area.

i. r = 7 cm, h = 10 cm

ii. r = 1.4 cm, h = 2.1 cm

iii. r = 2.5 cm, h = 7 cm

iv. r = 70 cm, h = 1.4 cm

v. r = 4.2 cm, h = 14 cm

Solution:

i. Given: r = 7 cm and h = 10 cm

To find: Curved surface area of cylinder and total surface area

Curved surface area of the cylinder = 2πrh

= 2 x \(\frac { 22 }{ 7 }\) x 7 x 10

= 2 x 22 x 10

= 440 sq.cm

Total surface area of the cylinder:

= 2πr(h + r)

= 2 x \(\frac { 22 }{ 7 }\) x 7(10 + 7)

= 2 x \(\frac { 22 }{ 7 }\) x 7 x 17

= 2 x 22 x 17

= 748 sq.cm

The curved surface area of the cylinder is 440 sq.cm and its total surface area is 748 sq.cm.

ii. Given: r = 1.4 cm and h = 2.1 cm

To find: Curved surface area of cylinder and total surface area

Curved surface area of the cylinder = 2πrh

= 2 x \(\frac { 22 }{ 7 }\) x 1.4 x 2.1

= 2 x 22 x 0.2 x 2.1

= 18.48 sq.cm

Total surface area of the cylinder = 2πr (h + r)

= 2 x \(\frac { 22 }{ 7 }\) x 1.4 (2.1 + 1.4)

= 2 x \(\frac { 22 }{ 7 }\) x 1.4 x 3.5

= 2 x 22 x 0.2 x 3.5

= 30.80 sq.cm

∴ The curved surface area of the cylinder is 18.48 sq.cm and its total surface area is 30.80 sq.cm.

iii. Given: r = 2.5 cm and h = 7 cm

To find: Curved surface area of cylinder and total surface area

Curved surface area of the cylinder = 2πrh

= 2 x \(\frac { 22 }{ 7 }\) x 2.5 x 7

= 2 x 22 x 2.5

= 110 sq.cm

Total surface area of the cylinder = 2πr(h + r)

= 2 x \(\frac { 22 }{ 7 }\) x 2.5 (7+ 2.5)

= 2 x \(\frac { 22 }{ 7 }\) x 2.5 x 9.5

= \(\frac { 1045 }{ 7 }\)

= 149.29 sq.cm

∴ The curved surface area of the cylinder is 110 sq.cm and its total surface area is 149.29 sq.cm.

iv. Given: r = 70 cm and h = 1.4 cm

To find: Curved surface area of cylinder and total surface area

Curved surface area of the cylinder = 2πrh

= 2 x \(\frac { 22 }{ 7 }\) x 70 x 1.4

= 2 x 22 x 10 x 1.4

= 616 sq.cm

Total surface area of the cylinder = 2πr(h + r)

= 2 x \(\frac { 22 }{ 7 }\) x 70(1.4 + 70)

= 2 x \(\frac { 22 }{ 7 }\) x 70 x 71.4

= 2 x 22 x 10 x 71.4

= 2 x 22 x 714

= 31416 sq.cm

∴ The curved surface area of the cylinder is 616 sq.cm and its total surface area is 31416 sq.cm.

v. Given: r = 4.2 cm and h = 14 cm

To find: Curved surface area of cylinder and total surface area

Curved surface area of the cylinder = 2πrh

= 2 x \(\frac { 22 }{ 7 }\) x 4.2 x 14 = 2 x 22 x 4.2 x 2

= 369.60 sq.cm

Total surface area of the cylinder = 2πr (h + r)

= 2 x \(\frac { 22 }{ 7 }\) x 4.2 (14+ 4.2)

= 2 x \(\frac { 22 }{ 7 }\) x 4.2 x 18.2

= 2 x 22 x 0.6 x 18.2

= 480.48 sq.cm

∴ The curved surface area of the cylinder is 369.60 sq.cm and its total surface area is 480.48 sq.cm.

Question 2.

Find the total surface area of a closed cylindrical drum if its diameter is 50 cm and height is 45 cm. (π = 3.14)

Given: For cylindrical drum:

Diameter (d) = 50 cm

and height (h) = 45 cm

To find: Total surface area of the cylindrical drum

Solution:

Diameter (d) = 50 cm

∴ radius (r) = \(\frac{\mathrm{d}}{2}=\frac{50}{2}\) = 25 cm

Total surface area of the cylindrical drum = 2πr (h + r)

= 2 x 3.14 x 25 (45 + 25)

= 2 x 3.14 x 25 x 70

= 10,990 sq.cm

∴ The total surface area of the cylindrical drum is 10,990 sq.cm.

Question 3.

Find the area of base and radius of a cylinder if its curved surface area is 660 sq.cm and height is 21 cm.

Given: Curved surface area = 660 sq.cm, and height = 21 cm

To find: area of base and radius of a cylinder

Solution:

i. Curved surface area of cylinder = 2πrh

∴ 660 = 2 x \(\frac { 22 }{ 7 }\) x r x 21

∴ 660 = 2 x 22 x r x 3

∴ \(\frac{660}{2 \times 22 \times 3}=r\)

∴ \(\frac{660}{2 \times 66}=r\)

∴ 5 = r

i.e., r = 5 cm

ii. Area of a base of the cylinder = πr²

= \(\frac { 22 }{ 7 }\) x 5 x 5

= \(\frac { 550 }{ 7 }\)

= 78.57 sq.cm

∴The radius of the cylinder is 5 cm and the area of its base is 78.57 sq.cm.

Question 4.

Find the area of the sheet required to make a cylindrical container which is open at one side and whose diameter is 28 cm and height is 20 cm. Find the approximate area of the sheet required to make a lid of height 2 cm for this container.

Given: For cylindrical container:

diameter (d) = 28 cm, height (h_{1}) = 20 cm

For cylindrical lid: height (h_{2}) = 2 cm

To find: i. Surface area of the cylinder with one side open

ii. Area of sheet required to made a lid

Solution:

diameter (d) = 28 cm

∴ radius (r) = \(\frac{\mathrm{d}}{2}=\frac{28}{2}\) = 14 cm

i. Surface area of the cylinder with one side open = Curved surface area + Area of a base

= 2πrh_{1} + πr²

= πr (2h_{1} + r)

= \(\frac { 22 }{ 7 }\) x 14 x (2 x 20 + 14)

= 22 x 2 x (40 + 14)

= 22 x 2 x 54

= 2376 sq.cm

ii. Area of sheet required to made a lid = Curved surface area of lid + Area of upper surface

= 2πrh_{2} + πr²

= πr (2h_{2} + r)

= \(\frac { 22 }{ 7 }\) x 14 x (2 x 2 + 14)

= 22 x 2 x (4 + 14)

= 22 x 2 x 18

= 792 sq cm

∴ The area of the sheet required to make the cylindrical container is 2376 sq. cm and the approximate area of a sheet required to make the lid is 792 sq. cm.