Summary on the last page
NUMERICALS ON MEASUREMENTS
I.
Do as directed – Area and Volumes
1. Harry was going on a vacation and was try to fit his scrabble board into his bag. Find out
how much space is required to fit the scrabble board in if it has a length of 4.5 cm and
breadth of 7cm.
Answer: The scrabble board is a rectangle
So space required to fit the scrabble board is nothing but the area of the rectangle
Thus area of a rectangle = length * breadth
= 4.5 cm * 7cm
= 31.5 cm2
Space required to fit the scrabble board = 31.5 cm2
2. Find the volume of a camera whose length is 6 cm, breadth 4 cm and height 1.4 cm.
Answer: The camera is a cuboid
So volume of the camera will be calculated using the formula for volume of a Cuboid
Thus volume of a Cuboid = length * breadth * height
= 6 cm * 4cm *1.4 cm
= 33.6 cm3
Volume of the camera = 33.6 cm3
3. Raju was presented with a gift box full of chocolates. Find the volume of the gift box if it
had a side of 8 cm.
Answer : Since only one dimension is given, we can understand that the gift box is a
cube.
So volume of the box will be calculated using the formula for volume of a cube
Thus volume of a cube = side * side * side
= 8cm * 8cm * 8cm
Volume of the gift box = 512cm3
= 512cm3
Summary on the last page
4. A building block has a length of 10mm, breadth of 6mm and height of 2mm. Find its
volume.
Answer : The building block is a cuboid.
So volume of the block will be calculated using the formula for volume of a cuboid
Thus volume of a Cuboid = length * breadth * height
= 10 mm * 6mm *2mm
= 120 mm3
Volume of the block = 120 mm3
5. An aquarium has a length of 6cm, breadth of 4cm and height of 3cm. Find the volume of
the aquarium.
Answer : The aquarium is a cuboid.
So volume of the aquarium will be calculated using the formula for volume of a cuboid
Thus volume of a Cuboid = length * breadth * height
= 6 cm * 4cm * 3cm
= 72 cm3
Volume of the aquarium – 72cm3
6. An architect needs to build a window measuring 35cm in length and 20 cm in breadth
on a wall. How much space does he need to mark on the wall for the window to fit in
correctly?
Answer : The window is a rectangle.
So the space he needs to mark on the wall for the window to fit in will be the area of the
window which will be calculated using the formula for area of a rectangle
Thus area of a rectangle = length * breadth
= 35 cm * 20cm
= 700 cm2
Space to be marked on the wall for the window to fit in = 700 cm2
Summary on the last page
7. Find the volume of a cupboard with side of 9 ft.
Answer: Since only one dimension is given, we can understand that the cupboard is a
cube.
So volume of the cupboard will be calculated using the formula for volume of a cube
Thus volume of a cube = side * side * side
= 9ft * 9ft * 9ft
= 729 ft3
Volume of the cupboard = 729 ft3
8. Sheela went to the cloth shop and asked for a square shaped cloth of length 7meters.
What is the area of the cloth Sheela bought?
Answer: Since the cloth was square shaped we know that length = breadth; in other
words it is the side. So area of the cloth will be calculated using the formula for area of a
square
Area of square = side * side
= 7m * 7m = 49m2
Area of the cloth = 49m2
II.
Do as directed – conversion of measurements
1. A farmer bought 440 ml of pesticide from a shop. If he sprayed 20 ml of pesticide twice
a day for his crops, how many days will the pesticide last?
Answer : Pesticide used each day = 20ml *2 ( since it is twice) = 40ml
Total pesticide bought = 440ml
Number of days the pesticide will last =
Total pesticide
Consumption each day
= 440ml
= 11 days
40ml
Answer = 11 days
Summary on the last page
2. A baker bought 6.5kg300g of sugar to bake cakes. How many grams of sugar did he buy
in all?
Answer – Total sugar bought by a baker = 6.5kgs 300g
So 6.5kgs needs to be converted to grams (since 300 is already in grams)
1kg
= 1000 grams
So 6.5 kgs =
?
= 6.5 * 1000 = 6500.0 grams = 6500 grams
So final answer = 6500 grams + 300grams = 6800 grams
Total sugar bought by the baker = 6800 grams
3. A tailor bought 60m25cm of cloth to stitch dresses? How many millimeters of cloth did
he buy in all?
Answer – Total cloth bought by the tailor = 60m25cm
First we need convert everything to cm and them to millimeter (since mm is smaller
than cm)
So 60m needs to be converted to cm (since 25 is already in cm)
1m
= 100cm
So 60 m =
?
= 60 * 100 = 6000 cm
Then; 6000 cm + 25cm = 6025 cm
Now cm needs to converted to mm
1cm = 100 mm
So 6025cm = ?
= 6025*100 = 602500 mm
Total cloth bought by the tailor = 6,02,500mm
Summary on the last page
4. A milkman gets a supply of 600litres of milk in a day. If he supplies 2 litres to each house
in a colony that has 220 houses per day, will he have any milk left with him at the end of
the day?
Answer : Milk supplied to the entire colony each day = 220 *2l( since there are 220
houses and each house gets 2l a day)
= 440 l
Total supply of milk the milkman gets = 600l
So since the consumption is only 440 l and he gets a supply of 600 l he will have milk
left with him.
5. A motorist filled 20 l 750 ml of petrol in his vehicle. How many ml of petrol did he fill in
all?
Answer – Total fuel filled by the motorist = 20 l 750 ml
So 20l needs to be converted to ml (since 750 is already in ml)
1l = 1000ml
So 20l =
?
= 20 * 1000= 20,000 ml
Then; 20,000ml + 750ml = 20,750ml
Total fuel filled by the motorist = 20,750ml
6. 23m450cm of cloth is required to decorate a stage. How many cms of cloth is required
in all?
Answer – Total cloth required = 23m 450cm
So 23m needs to be converted to cm (since 450 is already in cm)
1m
= 100cm
So 23 m =
?
= 23* 100 = 2300 cm
So, 2300 cm +450 cm = 2750cm
Total cloth required to decorate the stage = 2750cm
Summary on the last page
7. A merchant owns 600km25m of land. How many hectometers of land does he own?
Answer – Total land owned by the merchant = 600km25m
Step 1 : First we need to convert 600 km to hectometer since there is a direct
relationship between hectometer and kilometer
So 1 km = 10 hectometer
600 km = ?
= 600*10 = 6000 hectometer
Step 2 : Now 25m needs to be converted to decameter and then to hectometers
1 decameter
So
?
a)
= 10m
= 25m
= 25 *1 = 2.5 decameter
10
b)
10 decameter = 1 hectometer
2.5 decameter = ?
Then
= 2.5 ÷ 10 = 0.25 hectometers
c) So, 6000+ 0.25 = 6000.25 hectometers
Total land owned by the merchant = 6000.25 hectometers
8. A farmer sells 1quintal and 500g of seeds from his crops. How many grams of seeds did
he sell in all?
Answer – Total seeds sold by the farmer = 1quintal and 500g
So 1 quintal needs to be converted to grams (since 500 is already in grams)
1 quintal
= 100kg
1kg
= 1000 grams
So 100 kg =
?
= 100*1000 = 1,00,000 grams
So final answer = 1,00,000 + 500 = 1,00,500 grams
Answer : The farmer sold 1,00,500 grams of seeds
Summary on the last page
9. A cook bought 5kg of dhal at the beginning of a year. If he uses 5g of dhal in each of the
dishes he prepares and if he prepares 4 dishes a day, how many days will be dhal last
him?
Answer : Dhal used each day = 5 g *4 ( since he uses 5g in each dish and prepares 4
dishes a day) = 20g
Total dhal = 5kg = 5000 grams (since the consumption is in grams; 5kg has also to be
converted to grams. Kg CANNOT be divided by grams)
Number of days the dhal will last =
Total dhal bought
Consumption each day
= 5000 g
= 250 days
20 g
Answer = 250 days
10. A tanker can hold 800litres 60millilitres of water? How many milliliters of water can the
tank hold in all?
Answer – Total water a tanker can hold = 800litres 60millilitres
So 800 l needs to be converted to ml (since 60 is already in ml)
1l = 1000ml
So 800l =
?
= 800 * 1000= 8,00,000ml
Then; 8, 00,000ml + 750ml = 8,00,750ml
Total water the tank can hold = 8,00,750ml
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Summary on the last page
SUMMARY
All two dimensional figures will have area
• Area of a square = side * side
• Area of a rectangle = length * breadth * height
All three dimensional figures will have volume
• Volume of a cube = side * side * side
• Volume of a cuboid = length * breadth* height
Relationships between different units of length
10 millimeter = 1centimeter
10 centimeter = 1 decimeter
10 decimeter = 1 meter
10 meter = 1 decameter
10 decameter = 1 hectometer
10 hectometer = 1 kilometer
Relationships between different units of mass
1000 mg = 1 g
1000g = 1kg
100kg – 1 quintal
10 quintal = 1 metric ton
To convert from one unit to other , follow these steps
Example : To convert 100 cm to a decameter
First convert cm to decimeter and then to meter and then to decameter so that you don’t
miss steps
Step 1
10 cm
=
1 decimeter [Cross multiply and then divide]
100 cm
=
= 100 *1 = 10 decimeter
10
Step 2 10 decimeter = 1 meter
?
Summary on the last page
Step 3
10 meter
=
1 meter
=
1 decameter [Cross multiply and then divide]
?
= 1*1 = 0.1 decameter
10
So 100 cms = 0.1 decameter
If each step is followed, it will help in omitting errors and understanding the relationships
between different units of length easily.
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