Question 1:
The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the diameter of the base of the cylinder. Assume π =
Answer:
Height (h) of cylinder = 14 cm
Let the diameter of the cylinder be d.
Curved surface area of cylinder = 88 cm2
⇒ 2πrh = 88 cm2 (r is the radius of the base of the cylinder)
⇒ πdh = 88 cm2 (d = 2r)
⇒
⇒ d = 2 cm
Therefore, the diameter of the base of the cylinder is 2 cm.
Question 2:
It is required to make a closed cylindrical tank of height 1 m and base diameter 140 cm from a metal sheet. How many square meters of the sheet are required for the same?
Answer:
Height (h) of cylindrical tank = 1 m
Base radius (r) of cylindrical tank
Therefore, it will require 7.48 m2 area of sheet.
Question 3:
A metal pipe is 77 cm long. The inner diameter of a cross section is 4 cm, the outer diameter being 4.4 cm.
(i) Inner curved surface area,
(ii) Outer curved surface area,
(iii) Total surface area.
Answer:
Inner radius of cylindrical pipe
Outer radius of cylindrical pipe
Height (h) of cylindrical pipe = Length of cylindrical pipe = 77 cm
(i) CSA of inner surface of pipe
(ii) CSA of outer surface of pipe
(iii) Total surface area of pipe = CSA of inner surface + CSA of outer surface + Area of both circular ends of pipe
Therefore, the total surface area of the cylindrical pipe is 2038.08 cm2.
Question 4:
The diameter of a roller is 84 cm and its length is 120 cm. It takes 500 complete revolutions to move once over to level a playground. Find the area of the playground in m2?
Answer:
It can be observed that a roller is cylindrical.
Height (h) of cylindrical roller = Length of roller = 120 cm
Radius (r) of the circular end of roller =
CSA of roller = 2πrh
Area of field = 500 × CSA of roller
= (500 × 31680) cm2
= 15840000 cm2
= 1584 m2
Question 5:
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 Rs.12.50 per m2.
Answer:
Height (h) cylindrical pillar = 3.5 m
Radius (r) of the circular end of pillar =
= 0.25 m
CSA of pillar = 2πrh
Cost of painting 1 m2 area = Rs 12.50
Cost of painting 5.5 m2 area = Rs (5.5 × 12.50)
= Rs 68.75
Therefore, the cost of painting the CSA of the pillar is Rs 68.75.
Question 6:
Curved surface area of a right circular cylinder is 4.4 m2. If the radius of the base of the cylinder is 0.7 m, find its height.
Answer:
Let the height of the circular cylinder be h.
Radius (r) of the base of cylinder = 0.7 m
CSA of cylinder = 4.4 m2
2πrh = 4.4 m2
h = 1 m
Therefore, the height of the cylinder is 1 m.
Question 7:
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.
Answer:
Inner radius (r) of circular well
Depth (h) of circular well = 10 m
Inner curved surface area = 2πrh
= (44 × 0.25 × 10) m2
= 110 m2
Therefore, the inner curved surface area of the circular well is 110 m2.
Cost of plastering 1 m2 area = Rs 40
Cost of plastering 110 m2 area = Rs (110 × 40)
= Rs 4400
Therefore, the cost of plastering the CSA of this well is Rs 4400.
Question 8:
In a hot water heating system, there is a cylindrical pipe of length 28 m and diameter 5 cm. Find the total radiating surface in the system.
Answer:
Height (h) of cylindrical pipe = Length of cylindrical pipe = 28 m
Radius (r) of circular end of pipe = = 2.5 cm = 0.025 m
CSA of cylindrical pipe = 2πrh
= 4.4 m2
The area of the radiating surface of the system is 4.4 m2.
Question 9:
Find
(i) The lateral or curved surface area of a closed cylindrical petrol storage tank that is 4.2 m in diameter and 4.5 m high.
(ii) How much steel was actually used, if of the steel actually used was wasted in making the tank.
Answer:
Height (h) of cylindrical tank = 4.5 m
Radius (r) of the circular end of cylindrical tank =
(i) Lateral or curved surface area of tank = 2πrh
= (44 × 0.3 × 4.5) m2
= 59.4 m2
Therefore, CSA of tank is 59.4 m2.
(ii) Total surface area of tank = 2πr (r + h)
= (44 × 0.3 × 6.6) m2
= 87.12 m2
Let A m2 steel sheet be actually used in making the tank.
Therefore, 95.04 m2 steel was used in actual while making such a tank.
Question 10:
In the given figure, you see the frame of a lampshade. It is to be covered with a decorative cloth. The frame has a base diameter of 20 cm and height of 30 cm. A margin of 2.5 cm is to be given for folding it over the top and bottom of the frame. Find how much cloth is required for covering the lampshade.
Answer:
Height (h) of the frame of lampshade = (2.5 + 30 + 2.5) cm = 35 cm
Radius (r) of the circular end of the frame of lampshade =
Cloth required for covering the lampshade = 2πrh
= 2200 cm2
Hence, for covering the lampshade, 2200 cm2 cloth will be required.
Question 11:
The students of a Vidyalaya were asked to participate in a competition for making and decorating penholders in the shape of a cylinder with a base, using cardboard. Each penholder 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?
Answer:
Radius (r) of the circular end of cylindrical penholder = 3 cm
Height (h) of penholder = 10.5 cm
Surface area of 1 penholder = CSA of penholder + Area of base of penholder
= 2πrh + πr2
Area of cardboard sheet used by 1 competitor
Area of cardboard sheet used by 35 competitors
= = 7920 cm2
Therefore, 7920 cm2 cardboard sheet will be bought.