CYLINDER

  

1) The volume of a cylinder is 343π cm³ and height is 7cm. Find its lateral surface area.             7, 308

2) A solid cylinder has a total surface area is 231cm³. It's curved surface area is 2/3 of the total surface area. Find the volume of the cylinder.                        269.5cm³

3) Find the weight of a hollow cylinder lead pipe 26 cm and long 1/2 cm thick. Its external diameter is 5cm.(Weight of 1 cm³ of lead is 11.5 gm).                          2.114 kg

4) he diameter of a roller 120cm long is 84 cm. If it takes 500 complete revolutions to level a playground, determine the cost of levelling at the rate of 30 paise per per m² (π=22/7).                 ₹475.20

5) Two cylindrical pots contain the same amount of milk if their diameters are in the ratio 2:1, find the ratio of their heights.            1:4

6) Find 

A) the volume.                     2310cm³

B) whole surface area.        

of a right circular cylinder whose height is 15cm and radius of the base is 7 cm.                        968cm²

7) The diameter of the base of a right circular is 42cm and its height is 10cm. Find the area of the curved surface and the volume of the cylinder.            1320cm²,13860cm³.

8) Find the volume of a right circular cylinder which has a height a height of 21cm and the base radius of 5cm. Find also the curved surface area of the cylinder.                       1650cm³,660cm²

9) The curved surface area of a cylinder is 1320cm² and its base has a diameter 21cm. Find the height and the volume of the cylinder.                  20cm, 6930cm³

10) The volume of a cylinder is 69300cm³. and its height is 50cm. Find the area of the curved surface of the cylinder.                   6600cm²

11) The volume of a cylinder is 6358cm³and its height is is 28cm. Find its radius and the curved surface area.          1496cm²,8.5cm

12) The height of a cylinder is 10cm, and the ratio of its volume to its lateral surface is 3:2. Find its radius.                                       3cm

13) Find the curved surface area, the total surface area and the volume of the cylinder, the diameter of whose base is 7cm and height being 60cm. Also, find the capacity of the cylinder in litres.                 1320cm²,1397cm², 2310cm³.

14) The area of the curved surface of a cylinder is 4400cm² , and circumference of its base is 110cm. Find the height and the volume of the cylinder.          40cm, 38500cm³

15) A solid cylinder has total surface area of 462cm². Its curved surface area is one third of its total surface area. Find the volume of the cylinder.                        539cm³

16) The ratio between the curved surface area and the total surface total surface area of a right circular cylinder is 1:2. Find the volume of the cylinder, if total surface area is 616cm².                              1078cm³

17) If the radius of the base of a right circular cylinder is halved, keeping the height same , what is the ratio of the volume of the reduced cylinder to that of the original one.                                1:4

18) The radius of two cylinders are in the ratio 2:3 and their Heights are in the ratio 5:3. Calculate the ratio of their volume and the ratio of their curved surfaces.            20:27, 10:9

19) The radius and height of a cylinder are in the ratio 5:7 and its volume is 550cm³. find its radius.                                       5cm.

20) A solid cylinder has total surface area of 462cm². its curved surface area is one third of its total surface area. Find the volume of the cylinder.                           539cm³

21) How many cubic metres of Earth must be dug out to sink a well 14m deep and 4m in diameter? What will it cost to plaster its inner surface area at ₹2.50 per square metre?                                      ₹440

22) A rectangular piece of paper is 71cm long and 10cm wide. A cylinder is formed by Rolling the paper along its length. Find the volume of the cylinder. (Use π= 355/113).                        4011.5cm³

23) Two cylindrical vessels are filled with oil. The radius of one vessel is 15cm. and its height is 25cm. The radius and height of the Other vessel are 10cm. and 18cm. respectively. Find the radius of the cylinder vessel 30cm. in hight, which will just contain the oil of the two given vessels.            15.73cm.

24) The sum of the radius of the base and the height of a solid cylinder solid cylinder is 37m. If the total surface area of solid cylinder is 1628m², find the circumference of its base and the volume of cylinder.                      44m,4620m³

25) The cost of painting the total outside surface of a closed cylindrical oil tank at 25 paise per square decimeter is ₹77. The height of the tank is 3 times the radius of the base of the tank. Find its volume.                          404.25cm³

26) Find the cost of sinking a tubewell 280m deep having diameter 3m at the rate of ₹3.60 per m². Find also the cost of cementing its inner curved surface at ₹1.25 per m².                                           ₹3300

27) A 12m deep well with diameter 3.5 is dug up and Earth from it is spread evenly to form a platform 10.5m by 8.8m. Determine the height of the platform.         1.25m

28) A well with 10m inside diameter is dug 84m deep. Earth taken out of it is spread all around it up 7.5m to form an embankment. Find the height of embankment.                          1.6m

29) A path 2m wide surrounds a circular pond of diameter 40m. How many cubic metres of gravel are required to gravel the path to a depth of 20cm.                      52.8m³

30) The diameter of the roller 120cm. long is 84cm. If it takes 500 complete revolutions to level a playground of 30 paise per m².         ₹475.20

31) A cylindrical road roller made of iron is 1.5m long. Its inner diameter 54cm and the thickness of iron sheet rolled into the roller is 9cm. Find the weight of the roller, if 1cm³ of iron weighs 8 gm.       2138.4 kg

32) Find the number of coins 1.5cm. in diameter and 0.2cm. thick. to be melted to form a right circular cylinder of height 10cm and diameter 4.5cm.                       450

33) 25 circular plates, each of radius 10.5cm and thickness 1.6cm, are placed one above the other to form a solid right circular cylinder. find the curved surface area and the volume of the cylinderso formed.       2640cm²,13860cm³ 

34) The volume of a metallic cylindrical pipe is 748cm³. Its length is 14cm. its external radius is 9cm.find its thickness.          1cm

35) A hollow cylindrical copper pipe is 21dm long. its outer and inner diameters are 10cm and 6cm. respectively. Find the volume of the copper used fo the pipe.  10560cm³

36) A metal pipe has a bore(internal diameter) of 5cm. The pipe is 2mm thick all around. Find the weight in kilograms, of 2 metres of the pipe, if 1cm³,of the metal weight 7.7 gram.           5.033kg.

37) The difference between inside and outside surfaces of a cylindrical tube 14cm long is 88cm². if the volume of the cube is 176cm³. Find the inner and Outer radius of the tube.     1.5cm, 2.5cm

38) A cylindrical bucket 28cm. in diameter and 72cm. high is full of water. The water is emptied into a rectangular tank 66cm long and 28cm. Find the height of the water level in the tank.                   24cm.

39) A rectangular sheet of paper 30cm x 18cm. can be transformed into the curved surface of a right circular cylinder in two ways i.e., either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders thus formed.                                     5:3

40) What length of a solid cylinder 2cm in diameter must be taken to recast into a hollow cylinder of length 16cm, external diameter 20cm and thickness 2.5mm?    79 cm

41) A cylindrical container with diameter of base 56cm contains sufficient water to submerge a rectangular solid of iron with dimensions 32cm x 22cm x 14cm. Find the rise in the level of the water when the solid is submerged. 4cm.

42) Water flows out through a circular pipe whose internal diameter is 2cm, at the rate of 6 metres per second into a cylindrical tank, the radius of whose base is 60cm. By how much will the level of water rise in 30 minutes?            3m.

43) A cylindrical water tank of diameter 1.4m and height 2.1m is fed by a pipe of diameter 3.5cm through which water flows at the rate of 2cm/sec. Calculate in minutes the time it takes to fill the tank.                                  2800mins

44) Water is flowing at the rate of 3 km per hour through a circular pipe of 20cm internal diameter into a circular cistern of diameter 10m and depth 2m. In how many times will the cistern be filled? 1hr 40 min

45) Water flows out through a circular pipe whose internal diameter is 2 cm at the rate of 7 metres per second into a cylindrical tank the radius of whose base is 40cm By how much will be level of water rise in half an hour?       787.5 cm

46) A lead pencil consists of cylinder of wood with a solid cylinder of graphite fitted into it. The diameter of the pencil is 7cm. The diameter of the graphite is 1mm and the length of the pencil is 10cm. Calculate the weight of the whole pencil in grams correct to three places of decimals. If the specific gravity of the wood is 0.6 and of the graphite 2.3.                    2.443gm

47) Water flows out through a circular pipe whose internal diameter is 2cm at the rate of 7 metres per second into a cylindrical tank the radius of whose base is 40cm. By how much will the level of water rise of water rise in half an hour?                              787.5ccm

48) A well with 10m inside diameter is dug 14m deep. Earth taken out of it has been spread evenly around it, to a width of 5m.find the height of the embankment so formed.     14/3cm

49) A cylindrical pipe has inner diameter of 7cm and water flows through it at 192..5 litres per minute. Find in kilometre per hour, the rate of flow. (1 litre= dm³).                              3km/hr

50) The difference between inside and outside surfaces of a cylindrical metallic pipe 14cm long is 44cm². If the pipe is made of 99cm³ of metal, find the outer and inner radii of the pipe.   2.5cm, 2 cm

51) A copper wire 4mm in diameter 4mm in diameter is evenly wound about a cylinder whose length is 24cm and diameter 20cm so as to cover the whole surface. Find the length of the weight of the the wire assuming the specific gravity to be 88.8 gram per cm³.      426.24π² gm.