3rd Class Mathematics Measurement Length, Weight and Capacity Measurement of Capacity of Volume

        Measurement of Capacity or Volume of Liquid

 

The capacity of a container is the maximum quantity of liquid that container cancontain. If the capacity of a container is 1 litre then it means, it can hold the volume1 litre of liquid inside it. The standard unit for the measurement of liquid is litre.

The bigger volume of liquid is measured in litres and smaller volume in millilitre.

One litre is equal to 1000 millilitres. Therefore, one millilitre is thousandths part ofone litre. Litre is denoted by small letter of English alphabet I and millilitre is expressed in ml.

 

              Addition of Two or More Volume of Liquid

Addition by Conversion

The following steps are used for the addition of the volume of liquid:

Step 1:   Convert the volume into millilitres.

Step 2:   Add them by simple addition method.

Step 3:   Divide the resulting numbers of millilitres by 1000.

Step 4:   Whole part of the quotient of division is in litres and decimal part is inmillilitres.

 

Volume of petrol is 1 L 600 ml and kerosene is 2 L 200 ml. The sum of both the capacity is?

(a) 3 L 800 ml

(b) 3 L 700 ml

(c) 3 L 600 ml

(d) None of these

(e) All of these

 

Answer (a)

Explanation

1 L 600 ml = 1000 ml + 600 ml = 1600 ml and 2 L 200 ml = 2000 ml + 200 ml= 2200 ml. The sum of both the capacity = 1600 ml + 2200 ml = 3800 ml bydividing thousand  

 

           Addition without Conversion

The following steps are used for the addition of two volume:

Step 1:Arrange the volume vertically.

Step 2:Add by simple addition method from right.

Step 3:If carry is generated then add carry to the next addition.

  

 

A container contains 3 L 234 ml of milk and another container contains 1 L 766 ml of milk. Find the total capacity of both the containers?

(a) 31

(b) 51

(c) 11

(d) None of these

(e) All of these

 

Answer (b)

Explanation

 

 

              Subtraction of Two Volume of Liquid

Subtraction by Conversion

The following steps are used for subtraction of volume of liquid:

Step 1:   Convert the volume into millilitres.

Step 2:   Subtract by simple subtraction method.

Step 3:   Divide the resulting volume by 1000.

Step 4:   Whole part of the resulting volume is in litres and decimal part is in millilitres.

  

What should be subtracted from 5 L 600 ml to get 3 L 700 ml?

(a) 3 L 500 ml

(b) 11.900ml

(c) 9 L 300 ml

(d) None of these

(e) All of these

 

Answer (b)

Explanation

5 L 600 ml = 5000 ml + 600 ml = 5600 ml and 3 L 700 ml = 3000 ml + 700 ml= 3700 ml.

Hence, their different = 5600 ml - 3700 ml = 1900 ml =1L 900 ml

 

Subtraction without Conversion

The following steps are used for the subtraction of two capacity:

Step 1:   Arrange the capacity vertically.

Step 2:   Subtract by simple subtraction from right.

Step 3:   The resulting capacity is their difference.

 

The capacity of one gallon is 4 L 500 ml and another is 5 L 600 ml. What is the difference between the volume?

(a) 3 L 500 ml

(b) 5 L 500 ml

(c) 9L 300 mI

(d) None of these

(e) All of these

 

Answer (c)

Explanation

The difference of the volume = 5 L 600 ml - 4 L 500 ml

=1 L -100 ml    

 

             Multiplication of Volume

The following steps are used for the multiplication of the volume:

Step 1:   Arrange the volume vertically.

Step 2:   Multiply the volume by simple multiplication from right or ml.

Step 3:   Add them if multiplier is in two digits.

Step 4:   First three digit from the right of the product is in milliliters and remaining numbers are in liters.

 

   

If the volume of a container is 5 L 500 ml then what is the total volume of 3 such containers?

(a) 16 L 500 ml

(b) 6 L 500 ml

(c) 9 L 300 ml

(d) None of these

(e) All of these

 

Answer (a)

Explanations:

= 16 L 500 ml.    

 

             Division of the Volume

The following steps are used for the division of the volume:

Step 1:   Arrange the measured volume in division.

Step 2:   Divide by simple division method.

Step 3:   Quotient is the division of the volume.

 

   

Find the volume of each container if three containers to be filled completely by 50 L 600 ml of water.

(a) 16 L 867 ml

(b) 15 L 534 ml

(c) 19 L 322 ml

(d) None of these

(e) All of these

 

Answer (a)

       

= 16 L 866 ml.        

 

 

   

 

         What is the total volume of 34 L 200 ml petrol and 100 ml of lubricants?

(a) 34 L 300 ml

(b) 10 L 890 ml

(c) 20 L 120 ml

(d) None of these

(e) All of these

 

Answer (a)

Explanation

34 L 200 ml +100 ml = 34000 ml + 200 ml + 100 ml = 34300 ml = 34 L 300 ml.

 

   Add the following volume of liquid: 234 L 345 ml and 123 L 321 ml.

(a) 358 L 555 ml

(b) 357 L 666 ml

(c) 256 L 123 ml

(d) None of these

(e) All of these

 

Answers (b)

Explanation

34 L 345 ml + 123 L 321 ml = 234000 ml + 345 ml + 123000 ml + 321 ml =357666 ml = 357 L 666 ml.

 

          If 24 L 501 ml of milk is equally distributed among three containers then how much milk is distributed among the containers?

(a) 7 L 167 ml

(b) 8 L 160 ml

(c) 8 L 167 ml

(d) None of these

(e) All of these

 

Answer (c)

24 L 501 ml = 24501 ml - 3 = 8167 ml = 8.167 L = 8 L 167 ml.

 

       The volume of a container is 6200 L. Find the volume of a container made by fourth part of iron sheet of the given container?

(a) 1 L 550ml

(b) 1 L560ml

(c) 2 L 560 ml

(d) None of these

(e) All of these

 

Answer (a)

Explanation

Volume of fourth of the given container    

 

        There are five equal containers in a factory, the volume of every container is 534 L. What is the volume of exactly half of the volume of one container?

(a) 266L

(b) 265L

(c) 267 L

(d) None of these

(e) All of these

 

Answer (c)

Explanation

Half of the volume of container 534 L = 267 L.

 

          Distance between Mumbai and Delhi on the map is 10 cm. What is the actual distance between the cities according to the map if scale is 1 cm = 200km?

(a) 2000km

(b) 1000km

(c) 2010km

(d) None of these

(e) All of these

 

Answer (a)

Explanations:

Given scale is 1cm = 200 km. According to the map distance between the cities  

  

         If the length of a plane figure is 8 cm then how many length of one millimetre are there on the length of the plane figure?

(a) 8

(b) 80

(c) 16

(d) None of these

(e) All of these

 

Answer (b)

Explanations

 

  

       Length of a stick is 0.20 km. How many times it takes to complete the measurement of the length of 1 km?

(a) 2

(b) 3

(c) 5

(d) None of these

(e) All of these

 

Answer (c)

Explanation

Required number of times      

  

        Speed of a bus is 60 km/h. find the time taken by the bus to travel the distance of 100 m.

(a) 6 seconds

(b) 8 seconds

(c) 16 seconds

(d) None of these

(e) All of these

 

Answer (a)

Explanation

Bus travels the distance of 60 km in 60 minutes.

Hence, 1000 mini minute and 1 meterminute.

Thus the bus travels the distance of 100 m in  

 

          The length of a bus is 20 meters. How many buses are required to cover the distance of 1 km if they stands in que on the road?

(a) 60

(b) 50

(c) 40

(d) None of these

(e) All of these

 

Answer (b)

Required number of buses  

  

           The length of a tube is 100 centimetres. What will be the length of its 100th part in millimetre?

(a) 10 millimeters

(b) 100 millimeters

(c) 1000 millimeters

(d) None of these

(e) All of these

 

Answer (a)

The hundredth part of 100 cm is 1 cm and 1 cm = 10 mm.

 

          The height of a mobile tower is 225m 56cm. Which one of the following options is equal to the length of the tower in decimal number?

(a) 22556.34m

(b) 225.56m

(c) 225.560m

(d) None of these

(e) All of these

 

Answer (b)

Explanation

225 m and 56 cm = 225.56 m.

  

             A perpendicular line on a horizontal is 32 cm. What is the length of it half in metres?

(a) 0.18m

(b) 0.32m

(c) 0.16m

(d) None of these

(e) All of these

 

Answers (c)

Half of 32 cm = 16 cm. Hence,   

 

        The horizontal length of one side wall of a room is 8 m 5 cm and its al four walls are equal in horizontal length. What is the total length of the horizontal length of the room?

(a) 32.20m

(b) 16.10m

(c) 24.15m

(d) None of these

(e) All of these

 

Answer (a)

Explanation:  

A horizontal side of a wall is 8 m 5 cm = 805 cm; hence, the total length of horizontal sides  

  

         If the length of a book is 6 cm then the length of a book in metre will be?

(a) 0.6m

(b) 0.06m

(c) 0,006m

(d) None of these

(e) All of these

 

Answer (b)

Explanation  

  

       Find the total weight of 5 kg 500 grams rice, 10 kg 800 grams wheat and 3 kg 560 grams of pulse.

(a) 19 kg 860 grams

(b) 10 kg 890 grams

(c) 20 kg 200 grams

(d) None of these

(e) All of these

 

Answer (a)

Explanation

5 kg 500 grams + 10 kg 800 grams + 3 kg 560 grams = 19 kg 860 grams.

  

         The weight of one piece of apple is 300 grams. What is the weight of 12 same apples?

(a) 3 kg 500 grams

(b) 3 kg 600 grams

(c) 1kg 600 grams

(d) None of these

(e) All of these

 

Answer (b)

Explanations

The weight of 12 apples  

  

      What is the total weight of 510 grams of vegetables, 234 grams of curd and 120 grams of sugar?

(a) 920 grams

(b) 830 grams

(c) 864 grams

(d) none of these

(e) All of these

 

Answer (c)

Explanations

510 grams + 234 grams + 120 grams = 864 grams.

  

         What should be subtracted from 45 kg 140 grams to get 34 kg 200 grams?

(a) 10 kg 940 grams                         

(b) 9 kg 100 grams

(c) 6 kg 200 grams                           

(d) None of these

(e) All of these

 

Answer (a)

 

Explanation

Kg	Grams
45	140
?  34	200
10	940

                = 10 kg and 940 grams.  

  

         The weight of an object A is half of the weight of another object B. If the weight of B is 34 kg 23 grams then what is the weight of the object A?

(a) 14 kg 112 grams                         

(b) 15 kg 116 grams

(c) 17 kg 115 grams                         

(d) None of these

(e) All of these

 

Answer (c)

= 17 kg 115 grams.

 

 

 

• I. unit for the measurement of a length is meter.
• Millimetre is the smallest unit for the measurement of the length.
• One millimetre is the tenth part of one centimetre.
• One meter is the thousandth part of one kilometre.
• To express the two units in decimal number, place higher unit at left from decimal and lower unit at right from decimal.
• 1 mile = 1.63 km (approx.)
• 1 km = 1000 metres.
• To convert kilometers into metres multiply the number of kilometres by 1,000.
• To convert the kilometres and metres into metres multiply the number of kilometres by 1,000 and then add to the metres.
• Multiply higher unit to obtain lower unit and divide lower unit to obtain higher unit.

 

 

 

• Egyptian cubit is the first recorded unit for the measurement of length.
• The grain was the earliest unit for the measurement of mass.
• Metric system was first adopted by France.
• There are two types of Sl units basic and derived.
• International system of units is well accepted by every country in the world.
• Unit au means atomic unit which is used in atomic physics.