NCERT Solutions Class 5 Mathematics Chapter 14 How Big How Heavy

1. A stage platform is made with 5 Math-Magic books. The volume of this stage is the same as ______ cm cubes.
Ans. 546 cm.

2. Guess the volume of these things in cm cubes.

(a) A matchbox is about ___ cm cubes.
Ans. (a) 24 cm.

(b) A geometry box is about ___cm cubes.
Ans. (b) 90 cm.

(c) An eraser is about __ cm cubes.
Ans. (c) 6 cm.

2. How will you check your guess?
Ans. In case of matchbox: It is about 6 cm long, 4 cm wide and 1 cm thick. So, 6 x 4 x 1 i.e. 24 cm cubes will fit in it. Therefore, guess is correct.
In case of geometry box: It is about 16 cm long, 6 cm wide and 1 cm thick. So, 16 x 6 1 i.e. 96 cm cubes will fit in it.
In case of eraser: It is about 3 cm long, 2cm wide and 1 cm thick. So, 3 x 2 x 1 i.e. 6 cm cubes will fit in it.

3. Matchbox Play: 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.

(a) She used __ matchboxes to make this stage.
Ans. (a) 4 x 14 = 56.

(b) The volume of one matchbox is the same as 10 cm cubes. Then the volume of this stage is same as __ cm cubes.
Ans. (b) 560 cm.

(c) If all these cubes are arranged in a line, how long will that line be?
Ans. (c) 56 cm.

(d) Which has more volume- your Math-Magic book or Tanu’s platform?
Ans. (d) Tanu’s platform has more volume.'

4. With your friend’s collect many empty matchboxes of the same size.
Measure the sides and write here.

Ans. My matchbox is 3 cm wide. It is 5 cm long. It is 1 cm high.

5. Use 56 matchboxes to make platforms of different height. Fill this table.
Ans.

The volume of each platform if equal to 56 matchboxes.

6. Mohan arranged his matchboxes like this.
How many matchboxes did he use to make it? What is its volume in matchboxes? ___ matchboxes.
Ans. Mohan first puts 4 x 4 = 2=16 matchboxes on the lower most layer. In the second he puts 3 x 3 = 9 matchboxes. In the third he puts 2 x 2 = 4 matchboxes and 1 matchboxes on the top most layer.
Total number of matchboxes used = (16 + 9 +4 +1) = 30

7. How big is your cube?
(a) How long is the side of your cube?
Ans. a) The side of the cube is 7 cm.

(b) How many centimetres cubes can be arranged along its:
Length? _______
Width? _______
Height? ______
Ans. (b) Number of centimetres cubes that can be arranged along its:
Length = 7 Width= 7 and Height =7.

(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?
Ans. (c) 49 cm cubes are needed for the first layer.
7 such layers are needed to make the cube.

(d) So the total cm cubes = ____
Ans. d) The total cm cubes = 343.

(e) The volume of the paper cube is same as __ cm cubes.
Ans. (e) The volume of the paper cubes is same as 343 cm cubes.

8. Anan made big cube having double the side of your paper cube. How many of the your paper cubes will fit in it? Try doing by collecting all the cubes made in your class.
Ans. Side of Anan’s cube = 2 x 7 cm = 14 cm
In its first layer, we can arranged 2 x 2= 4 paper cubes (of side 7 cm). And 2 such layers of 4 paper cubes each can be packed. So, in Anan’s cube, we can arranged
4 x 2 = 8 cubes.

9. Ganesh and Dinga went to pack 4000 centimetre cubes in boxes. These are to be sent to a school. There are three different boxes available for packing.

(a) What is your guess? Who is right?
Ans. (a) I think Ganesh is right.

(b) How can Ganesh and Dinga test their guesses before packing the cubes in the boxes? Discuss with your friend.
Ans. (b) Ganesh and Dinga should find the number of cubes to be fitted in the first layer and find the number of layers to fill the cubes. Their products gives us the total number of cubes that can be packed in each cube. In this way, they are able to check up their guesses.

(c) Use Ganesh’s method and write:
_____ centimetre cubes can be arranged in box B.
_____ centimetre cubes can be arranged in box C.
Ans. (c) In first layer of box B, we can arrange 11 x 11 = 121 cubes. And 10 such layers of 121 cubes each can be packed. So, 121 x 10 = 1210 centimetre cubes can be arranged in box B.
In first layer of box C, we can arrange 15 x 9 = 135 cubes. And 10 such layers of 135 cubes each can be packed. So, 135 x 10 = 1350 centimetre cubes can be arranged in box C.

(d) So___ centimetre cubes in all can be packed in the three boxes.
Ans. (d) So, 2000 + 1210 + 1350 + = 4560 centimetre cubes in all can be packed in the three boxes.

10. (a) For 6 days, each person will need
Rice and flour __ g
Pulses ___ g
Dried onion __ g
Ans. (a) For 6 days, each person will need
Rice and flour = 6 x 200 = 1200 g
Pulses = (1200/3) = 400 g
Dried onions = 6 x 10 = 60 g

(b) How much of fresh tomatoes should be dried for 6 days for 10 people?
Ans. (b) Dried tomatoes need for 6 days for 10 people
= 6 x 10 x 10 = 600 g

(c) What is the total weight of food (for 6 days) in each person’s bag?
Ans. (c) The total weight of food (for 6 days) in each person’s bag
= 1200 g + 400 g + 60 g + 50 x 6 g + 50 x 6 g + 40 x 6 g + 10 x 6g + 40 x 6g + 5 x 6g + 10 x 6g
= (1200 + 400 + 60 + 300 + 240 + 60 + 240 + 30 + 60) = 2890 g

11. Can you guess the weight of the heaviest animal on this Earth? No, it’s not me. I weigh only 5000 kg! It is the Blue Whale. Its weight is around 35 times more than me. So how many thousand kg does it weight?
Ans. The weight of the blue whale = 35 x 5000kg = 175000 kg = 175 thousand kg.

12. Guess how many children of your weight will be equal to the weight of an elephant of 5000 kg.
Ans. Since my weight is 31 kg, I think that about 160 children of my weight will be equal to the weight of an elephant of 5000 kg.

13. 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?
Ans. Weight of a baby elephant at birth = 90 kg
My weight at the time of birth = 3 kg
Therefore, a baby elephant was 90/3 = 30 times heavier than me at birth.

14. If a grown up elephant eats 136 kg of food in a day than it will eat around __ kg in a month. Guess about how much it will eat in a year.
Ans. Weight of food eaten by a grown elephant in 1 day = 136 kg
Weight of food eaten by a grown elephant in 1 month i.e. 30 days = 136 x 30 kg = 4080kg
Weight of food eaten by a grown elephant in a year i.e. 12 months
= 4080 x 12 kg = 48960 kg

15. Shahid works in a bank. He sits at the cash counter. Whenever there are too many coins he does not them. He just weighs them. Can you hold these coins and say which is the heaviest?

(1) How many coins are there in a sack of 5 rupees coins if it weigh:

(a) 18 kg?
Ans. (a) Since 1 kg = 1000 g. So, 18 kg = 18000 g.
If one coin weights 9g, then the sack weighing 18000 g has 18000/9 = 2000 coins in it.

(b) 54 kg?
Ans. (b) Since 1 kg = 1000 g. So, 54 kg = 54000 g.
If one coin weights 9g, then the sack weighing 54000 g has 54000/9 = 6000 coins in it.

(c) 4500g?
Ans. (c) If one coin weighs 9g, then the sack weighing 4500 g has 4500/9= 500 coins in it.

(d) 2kg and 250g?
Ans. (d) 2 kg and 250 g = 2 x 1000g + 250 g = 2000 g + 250 g = 2250 g.
If one coin weighs 9g, then the sack weighing 2250 g has 2250/9 = 250 coins in it.

(e) 1 kg and 125 g?
Ans. (e) 1 kg and 125 g = 1 x 1000 g + 125 g = 1000 g + 125 g = 1125 g
If one coin weighs 9g, then the sack weighing 4500 g has 1125/9 = 125 coins in it.

(2) A 2 rupee coin weighs 6 g. What is the weight of a sack with:

(a) 2200 coins? ___ kg ____ g
Ans. (a) Weight of 2 rupee coins = 6 g
Weight of 2200 such coins = 2200 x 6 g = 13200 g = 13000 g + 200 g = 13 kg 200g

(b) 3000 coins? ____ kg
If 100 one rupee coins weigh 485 g then how much will 10000 coins weigh?
__ kg __ g.
Ans. (b) Weight of 2-rupee coins= 6 g
Weight of 3000 such coins =3000 6g = 18000 g = 18 x 1000 g = 18 kg
If 100 one-rupee coins weigh 485 g, then 10000 such coins weigh
= 485 x 100 g = 48500 g = 48 x 1000 g = 500 g = 48 kg 500 g

Question. The exact value of 1 US dollar compared to the Indian rupee changes from day to day. On a given day, Rs. 288 was worth 6 dollars. How many dollars would Rs. 480 have been worth on that day?
(a) 8
(b) 9
(c) 10
(d) 12

Answer : C

Question. What is the weight of the melon shown here?

(a) 2 kg
(b) 1kg 500g
(c) 2 kg 500 g
(d) 500g

Answer : B

Question. As an activity on measurement, a group of students was asked to measure the capacity of a bucket. Each used a different sized measuring-mug to measure the capacity of the container, filling the mug completely every time. The result is shown in the table :
Who used the biggest mug?

(a) Simran
(b) Isha
(c) Lakhsami
(d) Vasavi

Answer : A

Question. Study the wrapper of a packet of cheese slices shown below:
Which of the following CANNOT be found from the information on this wrapper?
(a) Price per slice
(b) Price of 150 ml milk
(c) Weight of one slice
(d) Volume of milk used for the contents of the packet

Answer : B

Question. Which of the following is likely to have a capacity of 200 litres?
(a) a cup or glass
(b) a pressure cooker
(c) a water tank
(d) a pond

Answer : C

Question. 4 full cans of juice when poured into an empty bowl give 6 litres of juice altogether.  
How many litres of juice would you have got from 6 full cans like these? 
(a) 12
(b) 9
(c) 8
(d) 4

Answer : B

Question. The weighing machine below is displaying the weight of the melon placed on it. How much does the melon weigh?

(a) 300g
(b) 750 g
(c) 1kg 100 g
(d) 1 kg 250 g

Answer : B

Question. According to the information on the pack, about how much would 2 litres of oil weigh at the temperature mentioned?

(a) 1 kg
(b) 1 kg 80 g
(c) 1 kg 800 g
(d) 18 kg

Answer : C

Question. How much water does the jar contain?

(a) 800 ml
(b) 1 li 50 ml
(c) 1li 200 ml
(d) 1 li 500 ml

Answer : D

Question. Arti bought ½ kilogram of sweets. How many grams did she buy?
(a) 200 grams
(b) 250 grams
(c) 500 grams
(d) 1000 grams

Answer : C

Question. The height of the tallest man in the world could be around:
(a) 1.5 m
(b) 2.4 m
(c) 3.6m
(d) 6.4m

Answer : B

Question. What is the sum of the lengths of all the edges of the given CUBE?

(a) 8 cm
(b) 12 cm
(c) 16 cm
(d) 24 cm

Answer : D

Question. In how many different ways can we combine the weights shown here to add up to 2kg? (Pairs of same weights are identical to each other).

(a) 2
(b) 4
(c) 4
(d) 5

Answer : B

Question. A beaker (vessel) is weighed when it is empty and when it  full of water. How much does the water in the beaker weigh? 

(a) 50 g
(b) 200 g
(c) 250 g
(d) 300 g

Answer : B

Question. If 300 ml of water is poured into each of these containers, in which one will the increase in height of the water be maximum?

Answer : A