Answer for Volume

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1.           Step 1 : 33 /5 = 6 R 3         3 x 22 x 20 = 1320     

                    Step 2 : 22 /5 = 4 R 2         33 - 3 = 3           2  x 30 x 20 = 1200
 
                    Step 3 : 1320 + 1200 = 2520 cm3

                    The volume of the space left in the box is 2520cm3

   

    2.            This is mathematics and not science, so presume the air cannot be compressed.

                   Step 1 : 1620 x 2/3 = 1080              1620 - 1080 = 540

                   Step 2 : 405 - 45 = 360

                   Step 3 : 540 / 360 = 1.5

                   It will take 1 minute and 30 seconds to fill the remaining space in the wheel.



   3.           2 cm = 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26

                 3 cm = 3, 9, 12, 15, 18, 21, 24, 27, 30

                 2cm and 3cm have the common number of 12, 18 and 24.

                 12 x 18 x 24 = 5184 cm3

                 The dimensions of the cuboid are 12cm by 18cm by 24cm.


    4.          A = 1 x 1 x1 = 1cm3                  B = 3 x 3 x 3 = 27cm3

                 27 - 1 = 26cm3

                 26 /1 x 100% = 2600%

                 The volume of cube B than that of cube A is 2600% larger.



     5.          Front face :  4 : 3   = 4 x 3 = 12       
                  8 x 6 = 48    therefore length = 8cm and width = 6cm

                  Side face is a square, therefore the side is 6cm

                  8 x 6 x 6 = 288 cm3

                  The volume of the cuboid is 288cm3

Question 10 - Ratio

• The ratio of Ahmad's age to Suri's age is 5 : 3 now. 4 years ago, the ratio was 7 : 4. How old is Ahmad now?

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Question - 10 Answer

                             Ahmad             :           Suri                       Different of age
Now                        5                   :              3          =   2     
                                   x3=15                         x3=9          x3       = 6


4 Years ago            7                    :              4          =  3      
                                  x2=14                         x2=8         x2        = 6
                             _______________________________________________
                                        1 unit                                  1 unit      = 4 years
                             _______________________________________________
15 x 4 = 60

Ahmad now is 60 years old.

Question 9 - Fractions

• A group of boys played only two types of sports during recess. 1/4 of them played badminton and 2/3 of them played football. 1/6 of the boys played both sports and 90 boys did not play any sports at all. How many boys were there?

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Question 9 - Answer

Both = 1/6 = 2/12

Badminton = 1/4 = 3/12              3/12 -2/12 = 1/12 ( Badminton only)

Football = 2/3 = 8/12                  8/12 - 2/12 = 6/12 ( Football only)

1- 1/12 -6/12 - 2/12 = 3/12         3/12 = 90 ( did not play any sport)

90/3 = 30/unit                              30 x 12 = 360

There were 360 boys.

Question 8 - whole numbers

• A delivery company charges $15 for every parcel delivered on time. There is no charge for parcels delivered late. The company will also compensate its customers $5 for every parcel delivered late. In January, the company made a profit of $35,880 after compensating for late delivery of parcels. For every 50 parcels delivered, 3 were late.
• (a) How many parcels were delivered late in January?
• (b) How much money was lost because of late delivery?

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Question 8 - Answer

1 set = 47 delivered parcels + 3 late parcels

        = 47 x 15 - 3 x 5

        = 705 - 15

        = 690

Number of set = 35,880/690 = 52 set

Number of late parcels = 52 x 3 = 156

(a) There were 156 parcels delivered late in January.


156 x ( 5 + 15 ) = 3120

(b) $3120 was lost because of late delivery.

Question 7 - Whole numbers

• Mdm Sim and Mdm Li wrapped a total of 3300 dumplings. Mdm Sim wrapped 5 dumplings for every 6 dumplings that Mdm Li wrapped. They were paid 20 cents for every dumpling wrapped. They earned an extra $2.50 for every 40 dumplings wrapped.
• (a) How many dumplings did Mdm Sim wrap?
• (b) How much did Mdm Sim earn?

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Question 7 - Answer

              Mdm Sim wrapped 5 + Mdm Li Wrapped 6 = 11
             
              3300/11 = 300

              5 x 300 = 1500

             (a) Mdm Sim wrapped 1500 dumplings.

              1500 x 0.2 = 300 (Each dumpling earn 20 cents)

              1500/40 = 37.50 ( units of every 40 dumplings)

               37 x 2.50 = 92.50 ( Earned extra for every 40 dumplings)

               300 + 92.50 = 392.50 ( Total earned)

               (b) Mdm Sim earned $392.50

Question 6 - Ratio

• At a sport stadium, the ratio of the number of females to the number of males was 5:7. The ratio of the number of girls to the number of women was 2:3. The ratio of the number of boys to the number of men was 4:5.

• (a) What fractio of the people in the sports stadium were girls and boys?
• (b) If there were 1512 more men than women, how many people were at the stadium ?

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Question 6 - Answer

Females : 5 x 9 = 45     Girls : 2 x 9 = 18     Women : 3 x 9 = 27

Girls + Women = Females = 18 + 27 = 45

Males : 7 x 9 = 63        Boys : 4 x7 = 28      Men : 5 x 7 = 35

Boys + Men = Males = 28 + 35 = 63

(a) Girls + Boys = 18 + 28 = 46      Total number : 45 + 63 = 108

46/108 = 23/54



(b) Men – Women = 35 -27 = 8 Units

8 Units = 1512        1 Unit = 189       Total Units = 45 + 63 = 108

108 x 189 = 20412

There were 20,412 people at the stadium.

Question 5 - Percentage

•  Mrs Molly baked 180 cupcakes. 55% of them were of chocolate flavour and the rest were of vanilla flavour. After selling some of the chocolate cupcakes the percentage of the chocolate cupcakes became 40%.

• (a) How many cupcakes were left?
• (b) How many chocolate cupcakes were sold?

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Question 5 - Answer

180 x 55% = 99 (C)


180 – 99 = 81 (V)

After selling some chocolate cupcakes, the chocolate cupcakes = 40%, therefore the vanilla cupcakes = 60%

81 = 60%

1.35 = 1%

135 =100%

(a) There were 135 cupcakes left.


135 x 40% = 54

99 -54 = 45

(b) There were 45 chocolate cupcakes sold.

Question 4 - Ratio

• Every month when John received his salary, he would give his father some money and spent the remaining amount of salary. The ratio of the amount of money John gave to his father to the amount spent on himself was 7 : 4. John spent his money on food and transport in the ratio 5 : 3 respectively. If he spent $580 more on food than on transport, what was the ratio of the amount of money spent on food to his salary?

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Question 4 - Answer

Step 1 :            Food : Transport = 5 : 3


                        5 – 3 = 2 Units ( more food than transport)

                        2 Units =580 1 Unit = 290

Step 2 :            290 x 5 = 1450 (Food) 290 x 3 = 870 (Transport)

                       1450 + 870 = 2320 ( John spent)

Step 3 :           Give : Spent = 7 : 4

                       4 Units = 2320 1 Unit = 580

Step 4 :           Total Salary = 7 + 4 = 11 Units

                      11 x 580 = 6380

Step 5 :          Food : Salary = 1450 : 6380 = 5 : 22

The ratio of the amount of money spent on food to his salary was 5 : 22.

Question 3 - Fraction

• Shawn and Michael had different number of stamps at first. After Shawn gave Michael 1/4 of his stamps. Michael had more stamps than him. Michael then gave Shawn 1/4 of his new number of stamps and they had 126 stamps each at the end. How many stamps did Shawn have at first?

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Question 3 - Answer

This question we have to work backward.


Step 1 : Michael : 126 = 3 units 42 = 1 unit (give Shawn)

                            126 + 42 = 168

Step 2 : Shawn : 126 – 42 = 84 = 3 units 28 = 1 unit ( give Michael)

                          84 + 28 = 112 ( initial stamps)

Step 3 : Michael : 168 – 28 = 140 ( initial stamps)

Shawn had 112 stamps at first.

Question 2 - Volume

• Water flows into a tank at the rate of 45l per minute. After 10 min, the tap is turned off and the tank is 0.6 filled with water.
• (a) How much more water is needed to fill it to the brim?
• (b) The water in the tank is then poured into containers each 1.5m long, 0.3m wide and 10cm high. How many such containers are needed?

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Question 2 - Answer

45 x 10 = 450 l

450 /6 = 75 l
75 l x 4 = 300 l

(a) 300 l more water is needed to fill it to the brim.



150cm x 30cm x 10cm = 45,000cm cube = 45l

450 / 45 = 10

(b) There are 10 containers are needed.

Question 1 - Percentage

• There are 20 pencils, rulers and pens in the pencil case. 25% of the total number of items are pens. There is 1 fewer ruler than pens. How many pencils are there in the pencil case?

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Question 1 - Answer

First, find the number of pens.

25% x 20 = 25/100 x 20
                = 1/4 x 20
                = 5
There are 5 pens in the pencil case.

Next, find the number of rulers.
5 - 1= 4
There are 4 rulers in the pencil case.

Then, find the number of pencils.
20 - ( 5+ 4 ) = 20 - 9
                    = 11
There are 11 pencils in the pencil case.