Answer for Volume

Click Here for the Question.

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?

Click Here for the answer.

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?

Click Here for the answer.

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?

Click Here for the answer.

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.