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8  Water is pouring into a cubiodal reservoir at the rate of 60 litres per minute. If the volume of reservoir is  108\ m^3 , find the number of hours it will take to fill the reservoir.

 

                                                                             

Given that the water is pouring into a cuboidal reservoir at the rate of 60 litres per minute. Volume of reservoir is , then The number of hours it will take to fill the reservoir will be: As we know . Then  = 108,000 Litres ; Time taken to fill the tank will be: or   .  

If each edge of a cube is doubled,

    (i) how many times will its surface area increase?

Surface area of cube  =   So if we double the edge l becomes 2l. New surface area =  Thus surface area becomes 4 times.

6  A milk tank is in the form of cylinder whose radius is 1.5 m and length is 7 m. Find the quantity of milk in litres that can be stored in the tank?

Volume of the cylinder = V =                                                 So the quantity of milk in litres that can be stored in the tank is 49500 litres.                                            

5. Find the height of the cylinder whose volume is 1.54 m 3 and diameter of the base is 140 cm ?

 

Given that the volume of the cylinder is  and having its diameter of base = 140cm. So, as ; hence putting in the relation we get; The height of the cylinder would be = .    

4. A cuboid is of dimensions 60 cm \times 54 cm \times 30 cm. How many small cubes with side 6 cm can be placed in the given cuboid?

So given the dimensions of cuboid  hence it's the volume is equal to =  We have to make small cubes with side 6cm which occupies the volume  =  Hence we have now one cube having side length = 6cm volume = . So, total numbers of small cubes that can be placed in the given cuboid =  Hence 450 small cubes can be placed in that cuboid.

3. Find the height of a cuboid whose base area is 180 cm 2 and volume is 900 cm 3?

Given that the height of a cuboid whose base area is  and volume is ; As  So, we have relation:  or, Height = 5cm.

2. Diameter of cylinder A is 7 cm, and the height is 14 cm. Diameter of cylinder B is 14 cm and height is 7 cm. Without doing any calculations can you suggest whose volume is greater? Verify it by finding the volume of both the cylinders. Check whether the cylinder with greater volume also has greater surface area?

Given the diameter of cylinder A = 7cm and the height = 14cm. Also, the diameter of cylinder B = 14cm and height = 7cm. We can easily suggest whose volume is greater without doing any calculations: As volume is directly proportional to the square of the radius of cylinder and directly proportional to the height of the cylinder hence  B has more Volume as compared to A because B has a larger...

1. Given a cylindrical tank, in which situation will you find surface area and in
which situation volume.

    (c) To find the number of smaller tanks that can be filled with water from it.

(c) We have to find out the volume.

1. Given a cylindrical tank, in which situation will you find surface area and in
which situation volume.

    (b) Number of cement bags required to plaster it.

(b) if we want to find out the cement bags required to plaster it means the area to be applied, we then calculate the surface area of the bags.

1. Given a cylindrical tank, in which situation will you find surface area and in
which situation volume.

    (a) To find how much it can hold.

(a) To find out how much the cylindrical tank can hold we will basically find out the volume of the cylinder.

Find the volume of the following cylinders.

(i) The volume of a cylinder given as =  . or given radius of cylinder = 7cm and length of cylinder = 10cm. So, we can calculate the volume of the cylinder =           (Take the value of  ) The volume of cylinder = .   (ii) Given for the Surface area =  and height = 2m . we have .  

Find the volume of the following cubes

(a) with a side 4 cm             (b) with a side 1.5 m

(a) Volume of cube having side equal to 4cm will be     or    . (b) When having side length equal to 1.5m then , .  

Find the volume of the following cuboids

(i) Volume of cuboid is given as: , So, Given that Length = 8cm, Breadth = 3cm, and height = 2 cm so, its volume will be = . Aslo for Given Surface area of cuboid  and height = 3 cm we can easily calculate the volume: ; So, Volume = 

Q10.    A company packages its milk powder in cylindrical container whose base has a diameter of 14 cm and height 20 cm. Company places a label around the surface of the container (as shown in the figure). If the label is placed 2 cm from top and bottom, what is the area of the label.

        

Area of label =  2πrh                       Here height is found out as = 20-2-2 = 16 cm. 

9    A road roller takes 750 complete revolutions to move once over to level a road. Find the area of the road if the diameter of a road roller is 84 cm and length is 1 m.

        

 

Area in one complete revolution of roller =  2πrh.                                                                 So area of road  

8.  The lateral surface area of a hollow cylinder is 4224 cm^{2}. It is cut along its height and formed a rectangular sheet of width 33 cm. Find the perimeter of rectangular sheet?

Lenght of rectangular sheet                                                So perimeter of rectangular sheet = 2(l + b)                                                       . Thus perimeter of rectangular sheet is 322 cm.

A closed cylindrical tank of radius 7 m and height 3 m is made from a sheet of metal. How much sheet of metal is required?

Total surface area of cylinder = 2πr (h + r)                                               

Q.6    Describe how the two figures at the right are alike and how they are different. Which box has a larger lateral surface area?

        

The two figures have same height.The diference between them is one is cylinder and another is cube. lateral surface area of cylinder =                                                                                                        lateral surface area of cube =                                                                                                                                ...

Daniel is painting the walls and ceiling of a cuboidal hall with length, breadth and height of 15 m, 10 m and 7 m respectively. From each can of paint  100 m^{2} of area is painted. How many cans of paint will she need to paint the room?

        

Total area painted by Daniel :                                                                                          (  Bottom surface is excluded.) So,  Area                                                  No. of cans of paint required                                                       Thus 5 cans of paint are required.

4.    Rukhsar painted the outside of the cabinet of measure 1 m \times 2 m \times 1.5 m. How much surface area did she cover if she painted all except the bottom of the cabinet.

        

Required area = Total area - Area of bottom surface Total area     Area of bottom surface   So required area = 
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