Exercise 10.2

1. A closed cylindrical tank of height 1.4 m. and radius of the base is 56 cm. is made up of a thick metal sheet. How much metal sheet is required (Express in square meters)?

Solution:

Height (h): 1.4 m = cm

Radius (r): 56 cm

Total Surface Area (TSA): 2πr(h + r) = 2 × 227217 × × ( + ) cm

= 2 × × × cm2

= cm2

= 6.9568695.68 m2 (since 1 m2 = 10000 cm2)

2. The volume of a cylinder is 308 cm3. Its height is 8 cm. Find its lateral surface area and total surface area.

Solution:

Volume (V): πr2h2π r h + 2π r2 = 308 cm3

Height (h): 8 cm

308: (22/7) × r2 × 8

r2= (308 × 7) / (22 × 8) =

r= √() = = cm

Lateral Surface Area (LSA): 2πrh = 2 × × × = cm2

Total Surface Area (TSA): 2πr(r + h) = 2 × × × ( + ) = cm2

Threfore the Lateral surface area is 176 cm2, total surface area is 253 cm2.

3. A metal cuboid of dimension 22 cm. x 15 cm. x 7.5 cm. was melted and cast into a cylinder of height 14 cm. What is its radius?

Solution:

Volume of cuboid: l × b × h = 22 × 15 × 7.5 = cm3

Volume of cylinder: πr2h2π r h + 2π r2 = 2475 cm3

Height (h): cm

2475= () × r2 ×

r2= 2475 / 44 =

r: √([[22542352]]) = 152162 = cm

Therefore the radius of the cylinder is 7.5 cm.

4. An overhead water tanker is in the shape of a cylinder has capacity of 61.6 cu.mts. The diameter of the tank is 5.6 m. Find the height of the tank.

Solution:

Volume (V): πr2h = m3

Diameter: m, Radius (r) = m

61.6: (227) × ()^2 × h

h: 61.6 / ((227) × × ) = 61.6 / = m

Therefore the height of the tank is 2.5 m.

5. A metal pipe is 77 cm. long. The inner diameter of a cross section is 4 cm., the outer diameter being 4.4 cm. Find its:

(i) inner curved surface area

(ii) outer curved surface area

(iii) Total surface area

Solution:

Length (h): cm

Inner diameter: cm, Inner radius (r) = cm

Outer diameter: 4.4 cm, Outer radius (R) = cm

(i) Inner curved surface area: 2πrh = 2 × × × = cm2

(ii) Outer curved surface area: 2πRh = 2 × × × = cm2

(iii) Total surface area: Inner CSA + Outer CSA + 2 × (Area of ring)

Area of ring: π(r2 - r2) = (22/7) × (^2 - ^2) = (22/7) × = cm2

Total surface area: + + 2 × = cm2

6. A cylindrical piller has a diameter of 56 cm and is of 35 m high. There are 16 pillars around the building. Find the cost of painting the curved surface area of all the pillars at the rate of ₹5.50 per 1 m2.

Solution:

Diameter: cm, Radius (r): cm = m

Height (h): m

Curved Surface Area (CSA) of one pillar: = 2 × (22/7) × 0.28 × 35 = m2

CSA of 16 pillars: 16 × 61.6 = m2

Cost of painting: 985.6 × = ₹

7. The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to roll once over the play ground to level. Find the area of the play ground in m2.

Solution:

Given

Diameter: cm, Radius (r): cm = m

Length (h): cm = m

CSA of roller: 2πrh = 2 × (22/7) × 0.42 × 1.2 = m2

Area covered in 500 revolutions: 500 × 3.168 = m2

8. The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find (i) its inner curved surface area (ii) The cost of plastering this curved surface at the rate of Rs. 40 per m2.

Solution:

Diameter: m, Radius (r): m

Depth (h): m

(i) Inner CSA: 2πrh = 2 × (22/7) × 1.75 × 10 = m2

(ii) Cost of plastering: 110 × = ₹

9. Find

(i) The total surface area of a closed cylindrical petrol storage tank whose diameter 4.2 m. and height 4.5 m.

(ii) How much steel sheet was actually used, if 1/12 of the steel was wasted in making the tank.

Solution:

Diameter: m, Radius (r): m

Height (h): m

(i) TSA: 2πr(r + h)2πrh = 2 × (22/7) × 2.1 × (2.1 + 4.5) = m2

(ii) Let total steel used be x. Then x - (1/12)x(1/12)x - x = 87.12

()x = 87.12

x = 87.12 × (12/11) = m2

10. A one side open cylinderical drum has inner radius 28 cm. and height 2.1 m. How much water you can store in the drum. Express in litres. (1 litre = 1000 cc.)

Solution:

Radius (r): cm

Height (h): m = cm

Volume: πr2h2πrh = (22/7) × 282 × 210 = cm3

Volume in litres: 517440 / 1000 = litres

11. The curved surface area of the cylinder is 1760 cm.^2 and its volume is 12320 cm3. Find its height.

Solution:

CSA: 2πrhπr^2h = cm2

Volume: πr^2h2πrh = cm3

Divide Volume by CSA: (πr^2h) / (2πrh) = 12320 / 1760

/2 =

r = cm

Substitute r in CSA: 2 × (22/7) × × h = 1760

= 1760

h = cm