Volume P6 Nanyang 2011 SA2 P2 Q15

15. A rectangular tank measuring 3 m by 3 m by 1.5 m was 1/3 filled with water. A tap was turned on to fill up with water at a rate of 18 l/min. Every 2 minutes after the tap was turned on, 6 l of water was poured from a pail into the tank. How long did it take for the rectangular tank to be completely filled with water? Leave your answer as a mixed number in its simplest form. [4 marks]
Answer given: 428 2/3 min

2/3 x 300 x 300 x150 =9 000 000 cm3 = 9 000 litres

   18 x 2     6        36         6

|---------|-----|----------|------|-----
   2 min     0       2 min      0

1 cycle (2 min) à 18 x 2 + 6  =  42 litres

9 000  litres  à  9000/42  x  2  ≈  214 cycles

9 000  -  214  x  42  = 12 litres

12/18 = 2/3 min

214 x 2 = 428 = min

428 + 2/3 = 428 2/3 min







It was 428 2/3 min.

Volume P6

Volume P6 Ang Mo Kio 2011 SA2 P2 Q46

Volume P6 Mee Toh 2011 SA2 P2 Q17

Volume P6 CHIJ 2011 SA2 P2 Q18

Volume P6 MGS 2011 SA2 P2 Q13

Volume P6 Nan Hua 2011 SA2 P2 Q16

Volume PSLE 2010 P2 Q18

Diagram given - Tank A, 60 cm by 10 cm by 40 cm, with a tap above it, was empty.

Diagram given - Tank B, 50 cm by 20 cm by 36 cm, with a tap above it, was filled with water.
At first, Tank A was empty and one third of Tank B was filled with water. Both taps were turned on at the same time and water from both taps flowed at the same rate of 1.2 litres per minute.
How long did it take for the height of the water to be the same in both tanks?
(1 litre = 1000 cm³)


1/3  x  36  =  12

60 x 10 x H  -->  50 x 20 x (H - 12)

1000 H  -  600 H  -->  12 000

H  -->  12 000 / 400  =  30

60  x  10  x  30  =  18 000

18 000 / 1 200  =  15  minutes

It took  15 minutes.


Alternative method
----------------------

60  x  10  :  50  x  20  =  3  :  5

2 u  -->  1/3  x  36  =  12 cm

5 u -->  5/2  x  12  =  30  cm

60  x  10  x  30  ÷  1200  =  15  cm

It took  15  minutes.

MGS 2010 P6 Prelim P2 Q17:

A tank contains some water up to a height of 10 cm. When 4 identical marbles are put into the tank, the water level rises by 8 cm. One marble is then removed from the tank and a metal block is put into the tank. The water level increases to 22 cm.
(a) Find the ratio of the volume of 1 marble to the metal block. [2 marks]
(b) If the base area of the tank is 450 cm², how much more is the volume of the metal block than that of two marbles? [3 marks]
[Answer given: (a) 1 : 3   (b) 900 cm³]



4 marbles  -->  8 cm

1 marble  -->  1/4  x  8  =  2 cm

8  -  2  =  6  cm

Metal block  -->  22  -  10  -  6 =  6 cm

2 : 6 = 1 : 3      Since base area of tank is the same

a) The ratio of the volume of 1 marble to the metal block is 1 : 3.


6  -  2 x 2  =  2 cm

450  x  2  = 900 cm3

b) The volume of the metal block is  900 cm3  more than 2 marbles.

Volume PSLE 2010 P1 Q22

22. What is 1.55 litres in millilitres?




1.55 x 1000  =  1550 ml

Volume P6 2010 SA2 Pei Chun P2 Q15

36 x 36 x 36 = 46656 cm3

46656/(72 x 24) = 27 cm

7 u  -->  27 + 15 = 42

8 u  -->  8/7  x 42 =  48 cm

72 x 24 x 48 = 82944 cm3

                    = 82.944 litres

It was 82.944 litres.

Volume P6 2010 SA2 NY P2 Q4

Volume P6 2010 SA2 Nanyang P2 Q 11

40 x 20 x 10 = 8000   Amount of water upto bottom of cube

12000 - 8000 = 4000 cm3   Amount of water from above bottom of cube

40 x 20 = 800

10 x 10 = 100

800 - 100 = 700 cm2   Area of water just above bottom of cube

4000 / 700 = 5.71  Height of water above bottom of cube

5.71 + 10 = 15.71 cm    Height of water

It was 15.71 cm.

Volume P6

Water from 3 taps was used to fill an empty water tank. Tap X, Tap Y, Tap Z could fill the tank completely in 3 hours, 4 hours, 5 hours respectively.
(a) What fraction of the tank was filled with water after half an hour when all taps were turned on at the same time? Give your answer in the simplest form.

Now, only Tap X and Tap Y were both turned on to fill another empty water tank. Immediately after 20 minutes, Tap Z was also turned on. Both Tap X and Tap Y were turned off at the same time after turning on for an hour and only Tap Z was left to fill the tank completely.
(b) How much longer would Tap Z take to fill the tank completely with water after both Tap X and Tap Y were turned off? Express your answer in terms of hours in its simplest form.
(a) 47/120 (b) 1 & 5/12 h


X + Y + Z : 1 h --> 1/3 + 1/4 + 1/5 = 47/60

                   1/2 h --> 1/2 x  4/60 = 47/120

a) It was 47/120.


60 - 20 = 40 min
            = 40/60 h
            = 2/3 h

Z : 1 h --> 1/5

     2/3 h --> 2/3 x 1/5 = 2/15

X + Y : 1 h --> 1/3 + 1/4 = 7/12

2/15 + 7/12 = 43/60

1 - 43/60 = 17/60

60/60 --> 5 h

17/60 --> 17/60 x 5 = 17/12 h
                                    = 1 5/12 h

b) It was 1 5/12 h.

Volume P6 2010 SA2 ACS P2 Q16

A tank measuring 80 cm by 60 cm by 55 cm was 1/5 filled with water. A tap was turned on to fill it up with water at a rate of 9 litres per min. Every 30 seconds after the tap was turned on, an iron ball with a volume 500 cm3 was dropped into the tank. How many iron balls would there be in the tank when the water level reached the brim? (Ans 42 iron balls)


4/5 x 80 x 60 x 55 = 211200 cm3

60 s --> 9000 cm3
30 s --> 30/60 x 9000 = 4500 cm3

1 set --> 4500 + 500 = 5000 cm3

211200 / 5000 = 42 sets (max) --> 42 iron balls


There were 42 iron balls.

Volume P6

A container filled with some water as shown in Figure A below has a rectangular base area of 10.4cm2. Figure B shows the same container being turned upside down.
(a) Find the capacity of the container in cm3, correct to 2 decimal places.
(b) If the water in the container is transferred to another cube-shaped container of capacity 90cm3, find the height of the water level in the cube-shaped container.

Assume 4.3 cm. [When assume other number < 4.6 cm, different volume will be obtained.]

4.6 x 10.4 = 47.84

4.3 x 10.4 = 44.72

47.84 - 44,72 = 3.12

7.8 x 10.4 = 81.12

81.12 + 3.12 = 84.24 cm3

a) It was 84.24 cm3.    < 128.96 cm3

90^(1/3) = 4.48   Not sure if this is covered in P6

47.84/90 x 4.48 = 2.38 cm

b) It was 2.38 cm.

Volume P6 2010 SA2 CHIJ P2 Q12

The base of an empty tank measures 64 cm by 25 cm. It was being filled with water from Tap A and Tap B at a rate of 4 litres per minute and 10 litres per minute respectively. Both taps were turned on at the same time and they took 8 minutes to fill up the tank completely. (a) What was the height of the tank? (b) How much longer would it take if Tap A alone is used to fill up the empty tank? [4 marks][Answer given: 70 cm, 20 min]


4 + 10 = 14 litres/min

14 x 8 = 112 litres

112 x 1000 / (64 x 25) = 70 cm

a) It was 70 cm.


112/4 = 28

28 - 8 = 20 min

b) It was 20 min longer.

Volume P6 2010 SA2 RGS P2 Q11

A tank with a square base of side 60 cm, 80 cm tall, was 1/3 filled with water. (a) Find the volume of water in the tank (b) At 1 p.m., a tap was turned on to drain water out a rate of 10 litres per minute. 6 minutes later, another tap was turned on to fill the tank at 12 litres per minute. Find the volume of water in the tank at 1.10 p.m. [4 marks][Answer given: 96 litres or 96000 cm3, 44 litres]


60 x 60 x 80 = 288000 cm3
                    = 288 l

1/3 x 288 = 96 l

a) It ws 96 litres.

6 x 10 = 60

96 - 60 = 36 l

12 - 10 = 2 litres/min

4 x 2 = 8 l

36 + 8 = 44 l

b) It was 44 litres.

Volume P6 2010 Maha Bodhi P2 Q13

In every minute, three times as much water flows out of Tap A as Tap B into two empty containers, X and Y.
After 20 minutes, Container X is 2/5 filled with water and the height of water level in Container X is the same as that of Container Y as shown in the diagram above.
a) What is the length of the base of Container X?
b) How many litres of water can Container X hold?


50 x 45 = 2250

2250/3 = 750

750/25 = 30 cm

a) It is 30 cm.


Information not complete to solve (b).

Volume P6 2010 SA2 Rosyth P2 Q13

A tank has a capacity of 480 litres. Its base is a rectangle which has a perimeter of 4m. The ratio of the length to the breadth of the rectangle is 3:2. (a) Find the height of the tank (b) The tank is ¾ filled with water. A tap drains water out in the tank at a rate of 5 litres per minute. How long will it take to drain half of the volume of water of the tank? [5 marks][Answer given: 50 cm, 36 min]


3 + 3 + 2 + 2 = 10

10 u --> 4 m
1 u --> 4/10 = 0.4 m

3 u --> 3 x 0.4 = 1.2 m
                       = 120 cm

2 u --> 2 x 0.4 = 0.8 m
                       = 80 cm

480 x 1000 / (120 x 80) = 50 cm

a) It was 50 cm.


3/4 x 480 = 360 l

1/2 x 360 = 180 l

180/5 = 36 min

b) It wsas 36 min.