Balbharti Maharashtra State Board Class 8 Maths Solutions covers the Practice Set 16.2 8th Std Maths Answers Solutions Chapter 16 Surface Area and Volume.
Surface Area and Volume Class 8 Maths Chapter 16 Practice Set 16.2 Solutions Maharashtra Board
Std 8 Maths Practice Set 16.2 Chapter 16 Solutions Answers
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.