Chapter 19 Surface Areas and Volume of a Circular Cylinder RD Sharma Solutions Exercise 19.1 Class 9 Maths
Chapter Name  RD Sharma Chapter 19 Surface Areas and Volume of a Circular Cylinder Exercise 19.1 
Book Name  RD Sharma Mathematics for Class 10 
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Related Study  NCERT Solutions for Class 10 Maths 
Exercise 19.1 Solutions
1. Curved surface area of a right circular cylinder is 4.4 m^{2} . If the radius of the base of the cylinder is 0.7 m, find its height.
Solution
Given that,
Radius of base of the cylinder e_{r} = 0.7 m
Curved surface area of cylinder = 4.4 m^{2} = 2Ï€rh
Let h be the height of the cylinder
WKT,
2Ï€rh = 4.4m^{2}
⇒ 2 ×3.14 ×0.7 ×h = 4.4
⇒ (4.4)h = 4.4
⇒ h = 1
∴ The height of the cylinder = 1m.
2. In a hot water heating system, there is a cylinder pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.
Solution
Given that
Height of cylinder = length of cylinder pipe = 28 m.
Radius (r) of circular end of pipe = 5/2 cm = 2.5 cm = 0.025 m
Curved surface area of cylindrical pipe = 2Ï€rh
= 2 × 3.14 ×0.025 ×28 = 4.4 cm
∴ The area of radiation surface of the system is 4.4 m^{2} or 44000cm^{2}
3. A cylindrical pillar is 50 cm in diameter and 3.5 m in height. Find the cost of painting the curved surface of the pillar at the rate of 12.50 per m^{2}
Solution
Given that
Height of the pillar = 3.5 m
Radius of the circular end of the pillar = 50/2= cm.
= 25 cm = 0.25 m
Curved surface area of pillar = 2Ï€rh
4. It is required to make a closed cylindrical tank of height 1 m and base diameter 1400 cm from a meal sheet. How many square meters of the sheet are required for the same ?
Solution
Height of the cylindrical tank(h) = 1 m
Base radius of cylindrical tank (r) = 140/2 m = 70 cm = 0.7 m
Area of sheet required  total surface area of tank = 2Ï€(r + h)
= 2 ×3.14 × 0.7 (0.7 + 1) m^{2}
= 4.4 ×1.7 m^{2}
= 7.48 m^{2}
∴ So, it will required 7.48 m^{2} of metal sheet.
5. A solid cylinder has total surface area of 462 cm^{2} . Its curved surface area is one  third of its total surface area. Find the radius and height of the cylinder.
Solution
We have
6. The total surface area of a hollow cylinder which is open from both sides is 4620 sq. cm, area of base ring is 115.5 sq. cm and height 7 cm. Find the thickness of the cylinder.
Solution
Let the inner radii of hollow cylinder ⇒ r cm
Outer radii of hollow cylinder ⇒ R cm
Then,
7. Find the ratio between the total surface area of a cylinder to its curved surface area, given that its height and radius are 7.5 cm and 3.5 cm.
Curved surface area = 2Ï€rh
Height (h) = 10 cm
The total surface area of a hollow metal cylinder = 338 IT cm^{2}
We know that
= 2 × 22/7 × 70(280 + 70)
= 154000 cm^{2}
Required cost = (154000 × 3.50)/1000 = Rs. 539
(i) inner curved surface area.
(ii) the cost of plastering this curved surface at the rate of Rs. 40 per m^{2}
Depth (n) of circular well = 10 m
= 2 × 22/7 × 1.75 × 10m^{2}
= (144 × 0.25 ×10)m^{2}
= 110 m^{2}
Cost of plastering 110 m^{2} area = Rs.(110 × 40)= Rs. 4400
⇒ 2 × 3.14 × 2.1 ×4.5 m^{2}
= 59.4 m^{2}
15. The students of a Vidyalaya were asked to participate in a competition for making and decorating pen holders in the shape of a cylinder with a base, using cardboard. Each pen holder was to be of radius 3 cm and height 10.5 cm. The Vidyalaya was to supply the competitors with cardboard. If there were 35 competitors, how much cardboard was required to be bought for the competition?
Solution
Area of car board sheet used by 35 competitors = 1584/7 × 35 cm^{2} = 7920 cm^{2}
Radius of the roller = D/2 = 0.84/2 = 0.42
Area covered by the roller on one revolution = covered surface area of roller
Area of the playground = 100 × Area covered by roller in one revolution
= (100 × 0.12 × 22 × 1.5)m^{2} = 396 m^{2}
Now,
Cost of leveling 1m^{2} = 50P = 50/100
Cost of leveling 396 m^{2} = 1/2 × 396 = Rs. 198
Hence, cost of leveling 396 m^{2} is Rs. 198
Radius of each pillar (r) = a/2 = 0.5/2 = 0.25 m.
Height of each pillar = 4m
Curved surface area of each pillar = 2Ï€rh
= 2 × 3.14 × 0.25 × 4m^{2}
= 44/7 m^{2}
Curved surface area of 20 pillars = 20 × 44/7 m^{2}
Given , cost of cleaning = Rs. 2.50 per square meter