Maharashtra State Board Class 8 Mathematics & Statistics Solutions Chapter 16 Surface Area and Volume Practice Set 16.2 - Digest Answers | Maharashtra Board Solutions

Practice Set 16.2 8th Std Maths Answers Chapter 16 Surface Area and Volume

Question 1 Maharashtra Board Solution

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 & Step-by-Step Answer:

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 x 7 x 10 = 2 x 22 x 10 = 440 sq.cm Total surface area of the cylinder: = 2πr(h + r) = 2 x x 7(10 + 7) = 2 x 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 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 x 1.4 (2.1 + 1.4)
= 2 x 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 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 x 2.5 (7+ 2.5)
= 2 x x 2.5 x 9.5
=
= 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 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 x 70(1.4 + 70)
= 2 x 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 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 x 4.2 (14+ 4.2)
= 2 x 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 Maharashtra Board Solution

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 & Step-by-Step Answer:

Diameter (d) = 50 cm ∴ radius (r) = = 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 Maharashtra Board Solution

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 & Step-by-Step Answer:

i. Curved surface area of cylinder = 2πrh ∴ 660 = 2 x x r x 21 ∴ 660 = 2 x 22 x r x 3 ∴ ∴ ∴ 5 = r i.e., r = 5 cm

ii. Area of a base of the cylinder = πr²
= x 5 x 5
=
= 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 Maharashtra Board Solution

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 (h1) = 20 cm For cylindrical lid: height (h2) = 2 cm To find: i. Surface area of the cylinder with one side open ii. Area of sheet required to made a lid

Solution & Step-by-Step Answer:

diameter (d) = 28 cm ∴ radius (r) = = 14 cm i. Surface area of the cylinder with one side open = Curved surface area + Area of a base = 2πrh1 + πr² = πr (2h1 + r) = 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
= 2πrh₂+ πr²
= πr (2h₂+ r)
= 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.

Chapter 16 Surface Area and Volume Practice Set 16.2 Solutions