class IX Surface area and volumes

                                                   class IX - surface area and volumes

                                                         MISCELLANEOUS 

1.The curved surface area of a right circular cylinder of height 14 cm is 88 cm2. Find the volume of

    cylinder.

2. The edge of a cube is 10.5 mm. Find its total surface area in cm2

3.The volume of a committee room is 5760 m3. Its length and breadth are 24 m and 20 m respectively.

Find the height of the room.

4.Wallpaper, 312 m long and 25 cm wide is required to cover the walls of a room. Length of the room

is 7 m and its breadth is twice its height. Determine the height of the room.

5.One iron solid is a cuboid of dimensions 30 cm × 30 cm × 42.6 cm. It is melted and cubes each of side

3 cm are moulded from it. Find the number of cubes formed.

6. A cylinder is 3 m high and the circumference of its base is 22 m. Find its curved surface area.

7.50 circular plates, each of radius 7 cm and thickness - cm, are placed one above another to form a

solid right circular cylinder. Find the total surface area and the volume of the cylinder so formed.

8.A reservoir is in the form of a rectangular parallelopiped (cuboid). Its length is 20 m. If 18 kl of water

is removed from the reservoir, the water level goes down by 15 cm. Find the width of the reservoir

(1 kL = 1 m3).

9.A godown is in the shape of a cuboid of size 8 m × 6 m × 3 m. If a bag of grain occupies a space of

0.65 m3, How many bags can be stored in the godown?

10. If V is the volume of cuboid of dimensions a, b, c and S is the surface area, then prove that

1/V =2/S(1/a+1/b+1/c).

11.The volume of a cylinder is 4487 cm3 and height 7 cm. Find its total surface area.

12.The radius and height of a cone are in the ratio 3 : 4. If its volume is 301.44 cm3, what is its radius?

13.How many spherical lead shots each 4.2 cm in diameter can be obtained from a rectangular solid of

lead with dimensions 66 cm, 42 cm and 21 cm? (Use T=22/7).

14.A solid sphere of radius 3 cm is melted and then cast into small spherical balls each of diameter

    0.6 cm. Find the number of small balls thus obtained.

15.If h, c and V are height, curved surface area and volume of a cone respectively, prove that

     3TVh3-c2h2+9V2=0.

16. A rectangular water tank of base 11 m × 6 m contains water upto a height of 5 m. If the water in the

    tank is transferred to a cylindrical tank of radius 3.5 m, find how high will the water level be in this

    tank (U s Tt = 22/7).

17.A wall is to be built across an open ground to cover a width (or breadth) of 10 m. The height of the

     wall is 4m and thickness of the wall is 24 cm. If this wall is to built up with bricks whose dimensions

    are 24 cm x 12 cm x 8 cm, how many bricks would be required?

18.A solid metallic sphere of diameter 28 cm is melted and recast into a number of smaller cones, each

    of diameter 42 cm and height 3 cm. Find the number of cones so formed.

19.Solid spheres of diameter 6 cm are dropped into a cylindrical beaker containing some water and are

     fully submerged. If the diameter of the beaker is 18 cm and the water rises by 40 cm, find the

     number of solid spheres dropped in the water.

20.Length of a room is one and half times of its breadth. The cost of carpeting the room at ₹3.25 per m2

     is ₹175.50 and cost of papering the walls at ₹1.40 per m2 is ₹240.80. If 1 door and 2 windows       occupy 8 m2, find the dimensions of the room.

21.A rectangular container, whose base is a square of side 5 cm stands on a horizontal table and holds

water upto 1 cm from the top. When a cube is placed in the water it is completely submerged. The

water rises to the top and 2 cubic cm of water overflows. Calculate the volume of the cube and also

the length of its edge.

22.A box with lid is made of 2 cm thick wood. Its external length, breadth and height are 25 cm, 18 cm

and 15 cm respectively. How many cubic cm of liquid can be placed in it? Also find the volume of the

wood used in it.

23.The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find the cost of plastering the curved

surface area at the rate of ₹40 per m2 (use Tt = 22/7).

24.The dimensions of a rectangular box are in the ratio 2 : 3 : 4 and the difference between the cost of

     covering it with sheet of paper at the rate of ₹4 and ₹4.50 per m2is ₹416. Find the dimensions of the

    box

25.Water is flowing at the rate of 3 km/hr through a circular pipe of 20 cm internal diameter into a

    circular cistern of diameter 10 m and depth 2 m. In how much time will the cistern be filled?

26.Water is flowing at the rate of 7 m/s through a circular pipe whose internal diameter is 20 cm into a

cylindrical tank, the radius of whose base is 40 cm. Determine the height of the water

level in tank after 1/2 hr.

27.The circumference of the base of 10 m high conical tent is 44 m. Calculate the length of canvas used

    in making the tent if width of canvas is 2 m.

28.Into a conical tent of radius 8.4 m and vertical height 3.5 m, how many full bags of wheat can be

emptied, if space for the wheat in each bag is 1.96 m3?

29.A sector of a circle of radius 12 cm subtends an angle of 120°. It is rolled up so that two bounding

radii are joined together to form a cone. Find the volume of the cone.

30.Water flows at the rate of 10 m/minute through a cylindrical pipe 5 mm in diameter. How long would

it take to fill a conical vessel whose diameter of the base is 40 cm and depth 24 cm?

31.How many metres of cloth 1 m 10 cm wide, will be required to make a conical circus tent whose

height is 12 m and the radius of whose base is 10 m? Also determine the cost of the cloth

at ₹7 per metre.

32.A village, having a population of 4000, requires 150 litres of water per head per day. It has a tank

measuring 20 m × 15 m × 6 m. For how many days will the water of this tank last?

33.A cylindrical tub of radius 16 cm contains water to a depth of 30 cm. A spherical iron ball is dropped

into the tub and thus level of water is raised by 9 cm. What is the radius of the ball?

34.The surface areas of a sphere and a cube are equal. Prove that their volumes are in the ratio

1:Vn/6.

35.The size of the base of a can full of kerosene is 20 cm x 20 cm and its height is 45 cm. The kerosene

of this can is poured into another cane having base of size 25 cm x 15 cm and height 50 cm.

Determine the height of the kerosene in the second can.

36.The radius and height of a cone are in the ratio 4 : 3. The area of the base is 154 cm2. Find the area

of the curved surface (Use Tt = 22/7)

37.Twenty seven copper spheres each of radius R and surface area S are melted to form a new sphere

with surface areas S'. Find (a) radius R of the new sphere, (b) ratio of S and S'.

38.Volume of a cube is 5832 m3. Find the cost of painting in total surface area at the rate of ₹3.50 per

square metre.

39.The length, breadth and height of a room are 5 m, 4 m and 3 m respectively. Find the cost of colour

washing its four walls and ceiling at the rate of ₹7.50 per square metre

40.How many cubic metres of earth must be dug out to sink a well 24 m deep and of diameter 7 m?

Also, find the cost of plastering the inner curved surface at ₹3 per square metre.

41.A solid sphere of radius 6 cm is melted into a hollow cylinder of uniform thickness. If the external

radius of the base of the cylinder is 5 cm and its height is 32 cm, find the uniform thickness of the

cylinder.

42.A right triangle with its side 5 cm, 12 cm and 13 cm is revolved about the side 12 cm. Find the volume of the solid so formed.

43.A solid iron rectangular block of dimensions 4.4 m 2.6 m and 1 m is cast into a hollow cylinder pipe

of internal radius 30 cm and thickness 5 cm. Find the length of the pipe.

44.The pillars of a temple are cylindrical shaped. If each pillar has a circular base of radius 25 cm and

height 10.5 cm, then find the quantity of concrete mixture used to build 30 such pillars. Also find the

cost of concrete mixture at the rate of ₹250 per cubic metre? (Take Tt = 22/7)

45.A storage tank is in the form of a cube. When it is full of water, the volume of water is 15.625 m3.

If the present depth of water is 1.3 m, find the volume of water already used from the tank.

46.Two solid spheres made of the same metal have weighs 5920 g and 740 g, respectively. Determine

the radius of the larger sphere, if the diameter of the smaller one is 5 cm.

47.A shopkeeper has one spherical laddoo of radius 5 cm. With the same amount of material, how many

laddoos of radius 2.5 cm can be made?