MATHS Class-5 NCERT Solutions, Chapter-14: How Big? How Heavy?
The chapter How Big? How Heavy? focuses on dealing with the volumes of given shapes. It helps the students to learn the volume contained in various shapes and how much liquid they can hold. It covers the topics: philosophy Volumes of Shapes and Objects philosophy Estimating Volumes philosophy Comparing Volumes philosophy Visualising Volume Occupied NCERT Math-Magic questions are answered in a simple and engaging manner. We have also related 'Learning Concepts and interactive worksheets with the solutions. Our 'Learning Beyond' segment caters to all the probable questions that a child might think out of curiosity. Download Chapter 14 How Big? How Heavy? in PDF format for free here.
Download the NCERT Solutions for How Big? How Heavy? in PDF
When the Earth Shook
A potato is nearly __________ marbles.
Do it by yourself. Answers may vary. A sample answer is:
A potato is nearly 10 marbles.
Now make a guess. Do you think the volume of 10 five-rupee coins will be more than that of 10 marbles?
Do it by yourself. Answers may vary. Volume of a thing is the amount of space it occupies. Guess if the volume of 10 five-rupee coins will be more than that of 10 marbles.
Guess the volume of each of these:
A ball is nearly __________ marbles.
Do it by yourself. Answers may vary. A sample answer is:
A ball is nearly 10 marbles.
An eraser is nearly __________ marbles.
Do it by yourself. Answers may vary. A sample answer is:
An eraser is nearly 2 marbles.
A pencil is nearly __________ marbles.
Do it by yourself. Answers may vary. A sample answer is:
A pencil is nearly 3 marbles.
Now put each thing in the measuring glass and check your guess. Try with different things like a matchbox, a stone, etc. and fill the table.
Do it by yourself. Answers may vary. Put the things in a measuring glass and check the actual volume of the things. Compare it with your guessed volume. A sample answer is:
a) What is the volume of 6 marbles? ________ mL.
b) What is the volume of 16 one-rupee coins? _________ mL.
c) The volume of 24 marbles is _________ mL.
d) The volume of 32 one-rupee coins is _________ mL.
e) Mollie puts some five-rupee coins in the measuring bottle. How many coins has she put in it:
if 30mLwater is pushed up? __________
if 60mLwater is pushed up?___________
a) Perform the following steps to get the volume of 6 marbles.
Step 1: Note down the initial level of water in your measuring bottle.
Step 2: Put 6 marbles in your measuring bottle and observe the change in the level of the water.
Step 3: Obtain the difference between the two levels of the water to get the volume of 6 marbles.
For example: If the initial level of water is 10 mL, and the final level is 17 mL, then the volume of 6 marbles will be equal to
17 - 10 = 7 mL.
b) Perform the following steps to get the volume of 16 one-rupee coins.
Step 1: Note down the initial level of water in your measuring bottle.
Step 2: Put 16 one-rupee coins in your measuring bottle and observe the change in the level of the water.
Step 3: Obtain the difference between the two levels of the water to get the volume of 16 one-rupee coins.
For example: If the initial level of water is 10 mL and the final level is 29 mL, then the volume of 6 marbles will be equal to 29 - 10 = 19 mL. c) The volume of 6 marbles is approximately 7 mL. We know that
6 × 4 = 24. Therefore, the volume of 24 marbles will be 7 × 4 = 28 mL. d) The volume of 16 one-rupee is approximately 19 mL. We know that 16 × 2 = 32. Therefore, the volume of 32 marbles will be
19 × 2 = 38 mL. e) Do it by yourself. Answers may vary.
First guess and then use your measuring bottle to find out the volume in mL of some other things.
Do it by yourself. Answers may vary based on the selection of the things and the guesses made by you. A sample answer is:
Guess how many litres of water your body will push up?
Answer this question on your own. The answers may vary based on your weight.
This is a cube whose sides are 1 cm each. Your Math-Magic book is 1 cm high. So guess how many such centimetre cubes will take the same space as your Math-Magic book?
Do it by yourself. Observe the space occupied by the Math-Magic book and 1 cube. Then guess how many such cubes will occupy the same space as that of the book. Answers may vary.
Hey, my Math-Magic book is about ____ cm long. So ____ cm cubes will fit along its length.
Take a ruler and measure the length of the Math-Magic book. The length is approximately 26 cm.
The length of the cube is 1 cm. Therefore, the correct answer is:
My Math-Magic book is about 26 cm long. So, 26 cm cubes will fit along its length.
And it is about ___ cm wide. So ____ cubes will fit along the width.
Take a ruler and measure the width of the Math-Magic book. The width is approximately 20 cm. The length of the cube is 1 cm. Therefore, the correct answer is:
My Math-Magic book is about 20 cm wide. So, 20 cm cubes will fit along its width.
So total ___ cm cubes will fit on the Math-Magic book.
26 cubes will fit along the length of the Math-Magic book.
20 cubes will fit along the width of the Math-Magic book.
Therefore, a total of 26 × 20 = 520 cubes will fit on the Math-Magic book.
Now if all these cubes are arranged in one line then how long will that line be? ______cm.
A total of 520 cubes will fit on the book. If these cubes are arranged in one line, then the line will be 520 cm long, as the length of each cube is 1 cm.
A lemon is nearly __________ marbles.
Do it by yourself. Answers may vary. A sample answer is:
A lemon is nearly 4 marbles.
Practice Time
Ganesh and Dinga want to pack 4000 centimetre cubes in boxes. These are to be sent to a school. There are three different boxes available for packing.
What is your guess? Who is right?
Guess on your own and answer. Observe the sides of each box and then make a guess who is right.
A stage (platform) is made with 5 Math-Magic books. The volume of this stage is the same as _____ cm cubes.
The volume of 1 Math-Magic book is approximately 520 cm cubes. Multiply 520 by 5 to get the volume of 5 Math-Magic books.
520 × 5 = 2600
Therefore, the volume of the stage is 2600 cm cubes.
Guess the volume of these things in cm cubes.
a) A matchbox is about _________ cm cubes.
b) A geometry box is about _______cm cubes.
c) An eraser is about __________ cm cubes.
d) How will you check your guess? Discuss.
a) Do it by yourself. Answers may vary. A sample answer is:
A matchbox is about 24 cm cubes.
b) Do it by yourself. Answers may vary. A sample answer is:
A geometry box is about 96 cm cubes.
c) Do it by yourself. Answers may vary. A sample answer is:
An eraser is about 2 cm cubes.
d) Use cm cubes to verify your answers.
Tanu is making a stage with matchboxes. She first puts 14 matchboxes like this in the first layer. She makes 4 such layers and her stage looks like this. She used _____ matchboxes to make this stage.
14 matchboxes are used in the first layer.
The total number of layers is 4.
Multiply 14 by 4 to get the total number of matchboxes used.
14 × 4 = 56
Therefore, she used 56 matchboxes to make the stage.
The volume of one matchbox is the same as 10 cm cubes. Then the volume of this stage is same as _____ cm cubes.
The total number of matchboxes used is 56.
The volume of 1 matchbox is 10 cm cubes.
Multiply 56 by 10 to get the total volume of the stage.
56 × 10 = 560
Therefore, the volume of the stage is the same as 560 cm cubes.
If all these cubes are arranged in a line, how long will that line be? _____ cm.
Since 560 cm cubes are used to make the stage, multiply 560 by 1 to get the length of line.
Therefore, the line will be 560 cm long.
Which has more volume — your Math-Magic book or Tanu’s platform?
The approximate volume of the Math-Magic book is 520 cm cubes, and Tanu’s platform is 560 cm cubes.
Therefore, Tanu’s platform has more volume.
With your friends, collect many empty matchboxes of the same size. Measure the sides and write here.
Do it by yourself. A sample answer is:
Use 56 matchboxes to make platforms of different heights. Fill this table.
Do it by yourself. Answers may vary. A sample answer is:
The volume of each platform is equal to ________matchboxes.
Each platform is made up of 56 matchboxes. Therefore, the volume of each platform is equal to 56 matchboxes.
The volume of each platform is equal to ________matchboxes.
Each platform is made up of 56 matchboxes. Therefore, the volume of each platform is equal to 56 matchboxes.
Make deep drawings of the platforms you have made.
Do it by yourself. Answers will vary according to the platforms made.
Mohan arranged his matchboxes like this.
How many matchboxes did he use to make it? What is its volume in matchboxes? ________ matchboxes.
The length and the width of the first layer is equal to 4 matchboxes. Therefore, the first layer has 4 × 4 = 16 matchboxes.
The length and width of the second layer is 3 matchboxes. Therefore, the second layer has 3 × 3 = 9 matchboxes.
The third layer has 4 matchboxes and the fifth layer has 1 matchbox.
Add 16, 9, 4, and 1 to get the total number of matchboxes.
16 + 9 + 4 + 1 = 30
Therefore, he used 30 matchboxes, and the volume is 30 matchboxes.
Collect empty matchboxes. Arrange them in an interesting way. Make a deep drawing of it.
Do it by yourself. Collect a few empty matchboxes and arrange them in a pattern. Answers may vary. One example is:
a) How long is the side of your cube? _______
b) How many centimetre cubes can be arranged along its:
Length? __________
Width? __________
Height? __________
c) Answer Thimpu's questions:
To make the first layer on the table how many cm cubes will I use?
How many such layers will I need to make a paper cube?
d) So the total cm cubes = ______
e) The volume of the paper cube is the same as __________ cm cubes.
a) Take a ruler and measure the length of the side of your cube. It is approximately equal to 7 cm.
b) The length, the width, and the height of the cubes are 7 cm each. So, 7 cm cubes can be arranged along each of its length, width, and height.
Length = 7 cm
Width = 7 cm
Height = 7 cm
c) To make the first layer on the table he should use 7 cm cubes.
He needs to make 7 such layers to make the paper cube.
d) The total number of cm cubes in the first layer is 7.
Multiply 7 by 7 to get the total cm cubes in one layer.
7 × 7 = 49
The total number of layers is 7.
Multiply 49 by 7 to get the total cm cubes.
49 × 7 = 343
So, the total cm cubes = 343
e) The total number of cm cubes used is 343. Therefore, the volume of the paper cube is the same as 343 cm cubes.
Anan made a big cube having double the side of your paper cube. How many of your paper cubes will fit in it? Try doing it by collecting all the cubes made in your class.
The side of the paper cubes is 7 cm. The side of the big block is double of the paper cubes. Therefore, the side of the big block is 2 × 7 = 14 cm
In the first layer of the big cube there can be 4 paper cubes each of side 7 cm. The height of the big cube is 14 cm. Therefore, there will be 2 layers as 7 + 7 = 14.
In 1 layer there are 4 paper cubes. Therefore, in 2 layers there will be
2 × 4 = 8 paper cubes.
Hence, 8 paper cubes will fit into the big cube.
How can Ganesh and Dinga test their guesses before packing the cubes in the boxes? Discuss with your friend.
Using the length and width of a box, they find the number of cubes in the first layer. Then they used the height of the box to find the number of layers.
Use Ganesh's method and write:
_____ centimetre cubes can be arranged in box B.
Step 1: The length and the width of box B is 11 cm. Multiply 11 by 11 to get the number of centimetre cubes that can fit in 1 layer of the box.
11 × 11 = 121
Step 2: The height of box B is 10 cm. Therefore, it will have 10 such layers. Multiply 121 by 10 to get the total number of centimetre cubes that can be fit in the box.
121 × 10 = 1210
Therefore, 1210 centimetre boxes can be arranged in box B.
_____ centimetre cubes can be arranged in box C.
Step 1: The length and the width of box C is 15 cm and 9 cm respectively. Multiply 15 by 9 to get the number of centimetre cubes that can fit in 1 layer of the box.
15 × 9 = 135
Step 2: The height of box C is 10 cm. Therefore, it will have 10 such layers. Multiply 135 by 10 to get the total number of centimetre cubes that can be fit in the box.
135 × 10 = 1350
Therefore, 1350 centimetre boxes can be arranged in box C.
So _____centimetre cubes in all can be packed in the three boxes.
Number of cubes that can be packed in box A is 1200.
Number of cubes that can be packed in box B is 1210.
Number of cubes that can be packed in box C is 1350.
Add 1200, 1210, and 1350 to get the total number of cubes that can be arranged in the three boxes.
1200 + 1210 + 1350 = 3760
So, 3760 centimetre cubes in all can be packed in the three boxes.
Guess which pipe can take more sand inside it. Hold it on a plate and pour sand inside to check your guess. Was your guess correct? Discuss.
Observe the size of the pipe and guess which pipe can hold more sand. The answer may vary based on your observation and guess.
Hold the pipes on a plate and pour sand into both the pipes and check which pipes holds more sand.
Find out which pipe can take the most sand inside it. So which pipe has the most volume?
Hold the pipes on the plate and pour sand inside both the pipes and check which pipes hold more sand. The pipe that can hold more sand has more volume.
The list of food each person will need for one day:
a) For 6 days, each person will need:
? Rice and flour - ____ g
? Pulses - _____ g
Dried onions - _____ g
Step 1: For 1 day each person requires 100 g of rice. Multiply 100 by 6 to get the rice required by each person for 6 days.
100 × 6 = 600
For 1 day each person requires 100 g of floor. Therefore, for 6 days each person will require 600 g of flour.
Step 2:
600 + 600 = 1200
Therefore, for 6 days each person will need 1200 g of rice and flour.
Step 3: Each person needs 1200 g of rice and flour.
The pulses required is 13 of the weight of rice and flour. Divide 1200 by 3.
1200 ÷ 3 = 400
Therefore, for 6 days each person will need 400 g of pulses.
Step 4: The list shows that for 1 day each person requires 10 g of dried onions. Multiply 10 by 6 to get the dried onions required by each person for 6 days.
10 × 6 = 60
Therefore, for 6 days each person will require 60 g of dried onions.
b) How much of fresh tomatoes should be dried for 6 days for 10 people?
One person requires 10 g of dried tomatoes for 1 day.
Step 1: Multiply 10 by 10 to get the amount of dried tomatoes required by 10 people for 1 day.
10 × 10 = 100
Step 2: Multiply 100 by 6 to get the amount of dried tomatoes required by 10 people for 6 days.
100 × 6 = 600
Step 3: For 100 g dried tomatoes 1 kg of fresh tomatoes is required.
We know that 1000 g = 1 kg. Therefore, for 100 g dried tomatoes 1000 g of fresh tomatoes is required. Multiply 1000 by 6 to get the amount of fresh tomatoes required for 600 g dried tomatoes.
1000 × 6 = 6000
Therefore, 6000 g of fresh tomatoes is required by 10 people for 6 days.
A 2 rupee coin weighs 6 g. What is the weight of a sack with:
b) 3000 coins? ______ kg
Step 1: Weight of one 2-rupee coin is 6 g. Multiply 3000 by 6 to get the weight of 3000 coins.
3000 × 6 = 18000
So, 3000 coins weigh 18000 grams.
Step 2: We know that 1000 g = 1 kg. Divide 18000 by 1000 to convert 18000 g into kg.
18000 ÷ 1000 = 18
Hence, 3000 coins weigh 18 kg.
It is the Blue Whale. Its weight is around 35 times more than me. So, how many thousand kg does it weight?
The weight of an elephant is 5000 kg.
The weight of the Blue Whale is 35 times the weight of an elephant. Multiply 35 by 5000 to get the weight of the Blue Whale.
35 × 5000 = 175000
Therefore, the weight of the Blue Whale is 175 thousand kg.
Guess how many children of your weight will be equal to the weight of an elephant of 5000 kg.
The answer may vary based on your weight. Divide 5000 by your weight to get the number of children of your weight that will be equal to the weight of an elephant of 5000 kg.
For example: Let us consider your weight as 40 kg. Divide 5000 by 40 to get the number of children.
5000 ÷ 40 = 125
Therefore, if your weight is 40 kg then 125 children of your weight will be equal to the weight of an elephant of 5000 kg.
At birth, a baby elephant weighs around 90 kg. How much did you weigh when you were born? Find out. How many times is a baby elephant heavier than you were at birth?
The answer may vary based on your weight when you were born. Divide 90 by your weight when you were born to get the number of times the baby elephant is heavier than you were at birth.
For example: Let us consider your weight at birth was 3 kg. The weight of the baby elephant is 90 kg. Divide 90 by 3 to get the number of times the baby elephant is heavier than you were at birth.
90 ÷ 3 = 30
Therefore, the baby elephant is 30 times the weight of yours when you were born.
If a grown-up elephant eats 136 kg of food in a day then it will eat around _________ kg in a month.
An elephant eats 136 kg of food in 1 day.
There are 30 days in a month. Multiply 136 by 30 to get the amount of food that the elephant will eat in a month.
136 × 30 = 4080
So, it will eat around 4080 kg in a month.
Guess about how much it will eat in a year.
An elephant eats around 4080 kg in a month.
There are 12 months in a year. Multiply 4080 by 12 to get the food it will eat in a year.
4080 × 12 = 48960
Therefore, it will eat around 48960 kg in a year.
Guess about how much it will eat in a year.
An elephant eats around 4080 kg in a month.
There are 12 months in a year. Multiply 4080 by 12 to get the food it will eat in a year.
4080 × 12 = 48960
Therefore, it will eat around 48960 kg in a year.
Can you hold these coins and say which is the heaviest?
Do it by yourself. Hold each coin in your hand and try to guess which is the heaviest. The five rupees coin is the heaviest.
One kg is equal to 1000 g so 9 kg is equal to 9000 g. If one coin weighs 9 g then the bag weighing 9000 g has 9000 ÷ 9 = ______ coins in it. Easy!
The bag weighing 9000 g has 9000 ÷ 9 = 1000 coins in it.
How many coins are there in a sack of 5 rupee coins if it weighs:
a) 18 kg
Step 1: We know that 1000 g = 1 kg. Multiply 18 by 1000 to convert 18 kg into grams.
18 × 1000 = 18000
Step 2: One 5 rupee coin weighs 9 g. Divide 18000 by 9 to get the number of 5 rupee coins in the sack weighing 18 kg.
18000 ÷ 9 = 2000
Therefore, there are 2000 five rupee coins in a sack of 18 kg.
How many coins are there in a sack of 5 rupee coins if it weighs: b) 54 kg
Step 1: We know that 1000 g = 1 kg. Multiply 54 by 1000 to convert 54 kg into grams.
54 × 1000 = 54000
Step 2: One 5-rupee coin weighs 9 g. Divide 54000 by 9 to get the number of 5-rupee coins in the sack weighing 54 kg.
54000 ÷ 9 = 6000
Therefore, there are 6000 coins of 5 rupee in a sack of 54 kg.
How many coins are there in a sack of 5 rupee coins if it weighs: c) 4500 g
One 5 rupee coin weighs 9 g. Divide 4500 by 9 to get the number of 5 rupee coins in a sack weighing 4500 g.
4500 ÷ 9 = 500
Therefore, there are 500 coins of 5 rupee in a sack of 4500 g.
How many coins are there in a sack of 5 rupee coins if it weighs: d) 2 kg 250
Step 1: We know that 1000 g = 1 kg. Multiply 2 by 1000 to convert 2 kg to grams.
2 × 1000 = 2000
Therefore, 2 kg 250 g = 2000 g + 250 g = 2250 g.
Step 2: One 5-rupee coin weighs 9 g. Divide 2250 by 9 to get the number of 5-rupee coins in a sack weighing 2250 g.
2250 ÷ 9 = 250
Therefore, there are 250 coins of 5 rupee in a sack of 2 kg 250 g.
How many coins are there in a sack of 5 rupee coins if it weighs: e) 1 kg 125 g
Step 1: We know that 1000 g = 1 kg. Therefore, 1 kg 125 g = 1000 g + 125 g = 1125 g.
Step 2: One 5-rupee coin weighs 9 g. Divide 1125 by 9 to get the number of 5-rupee coins in a sack weighing 1125 g.
1125 ÷ 9 = 125
Therefore, there are 125 coins of 5 rupee in a sack of 1 kg 125 g.
A 2 rupee coin weighs 6 g. What is the weight of a sack with:
a) 2200 coins ? _____ kg _____ g
Step 1: Weight of one 2-rupee coin is 6 g. Multiply 2200 by 6 to get the weight of 2200 coins.
2200 × 6 = 13200
So, 2200 coins weigh 13200 gram which can be written as 13000 g + 200 g.
Step 2: We know that 1000 g = 1 kg. Divide 13000 by 1000 to convert 13000 g to kg.
13000 ÷ 1000 = 13
Hence, 2200 coins weigh 13 kg 200 g.
If 100 one rupee coins weigh 485 g then how much will 10000 coins weigh? _____ kg _____ g.
Step 1: 100 one-rupee coins weigh 485. Multiply 485 by 100 to get the weight of 10000 coins.
100 × 485 = 48500
Therefore, 10000 coins weigh 48500 g which can be written as
48000 + 500.
Step 2: We know that 1000 g = 1 kg. Divide 48000 by 1000 to convert 48000 g into kg.
48000 ÷ 1000 = 48
Hence, 10000 coins weigh 48 kg 500 g.
How do people who cannot see make out different notes and coins? (Hint: Look for a shape etc. on notes of Rs 20, 50, 100, 500 etc. and feel it.)
The people who cannot see can feel the different shapes on the notes and the coins and also observe the sizes of the different notes and coins to differentiate.
What should we look for to check if a 100-rupee note is real or fake?
We should check the size, the quality of the paper, and the different shapes on the notes and the way the numbers are written on the note to check if a 100-rupee note is real or fake.
Cut along the dark lines. Paste the shape on a thick paper. Fold along the dotted lines to get a sweet box as shown on page 126.
Perform the activity on your own. Take a pair of scissors and cut along the dark lines then start folding along the dotted lines to make a sweet box.
c) What is the total weight of food (for 6 days) in each person’s bag?
Step 1: For 6 days each person will need 600 g of rice, 600 g of flour, 400 g of pulses, 60 g of dried onions, and 60 g of dried tomatoes.
Step 2: For 1 day each person needs 50 g of oil. Multiply 50 by 6 to get the amount of oil required by each person for 6 days.
50 × 6 = 300
Step 3: For 1 day each person needs 50 g of sugar. Therefore, for 6 days each person will need 300 g of sugar.
Step 4: For 1 day each person needs 40 g of milk powder. Multiply 40 by 6 to get the amount of milk powder required by each person for 6 days.
40 × 6 = 240 g
Step 5: For 1 day each person needs 10 g of tea. Multiply 10 by 6 to get the amount of tea required by each person for 6 days.
10 × 6 = 60
Step 6: For 1 day each person needs 40 g of Dalia. Therefore, for 6 days each person will need 240 g of Dalia.
Step 7: For 1 day each person needs 5 g of salt. Multiply 5 by 6 to get the amount of salt required by each person for 6 days.
5 × 6 = 30
Step 8: Make a list of all the food items required for 6 days.
| Food | Weights in gram |
| Rice | 600 |
| Flour | 600 |
| Pulses | 400 |
| Oil | 300 |
| Sugar | 300 |
| Milk powder | 240 |
| Tea | 60 |
| Dalia | 240 |
| Salt | 30 |
| Dried onions | 60 |
| Dried tomatoes | 60 |
Step 8: Add the weight of each food item in the above table to get the total weight of the food.
600 + 600 + 400 + 300 + 300 + 240 + 60 + 240 + 30 + 60 + 60 = 2890
Therefore, the total weight of food (for 6 days) in each person’s bag is 2890 g.
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