Q&A - PSLE Math

[stary]

ksi:

stary:

Hi all,

Have a problem here...

A pail contains some pebbles and water. The total volume of the pebbles and water in the pail is 2300 cm3. A cube-shaped tank containing some water has a base area of 361 cm2. The ratio of the volume of water in the tank to the total volume of pebbles and water in the pail is 3:5. What is the water level in the tank? Give your answer in cm, correct to 2 decimal places.

When all the pebbles are transferred fro the pail to the cube-shaped tank, the total volume of water and pebbles in the tank becomes 2282.5 cm3.

(a) Find the increase in water level of the tank in cm.
(b) A stick is 13cm long. If the stick just touches the water surface in the cube-shaped tank vertically, find the length of the stick that is exposed outside the tank.

Vol of water in tank : vol of pebbles and water = 3 : 5
3: 5 = V : 2300
V = 3/5 x 2300 = 1380
Base area of tank = 361
Hence water level = 1380/361 = 3.82cm

Is there missing information? Something must happen to cause an increase in the water level to solve (a), eg, the pail's water and pebbles poured into the cube??

Hi ksi, i've added the missing info...

[corneyAmber]

stary:

ksi:

[quote=\"stary\"]Hi all,

Have a problem here...

A pail contains some pebbles and water. The total volume of the pebbles and water in the pail is 2300 cm3. A cube-shaped tank containing some water has a base area of 361 cm2. The ratio of the volume of water in the tank to the total volume of pebbles and water in the pail is 3:5. What is the water level in the tank? Give your answer in cm, correct to 2 decimal places.

When all the pebbles are transferred fro the pail to the cube-shaped tank, the total volume of water and pebbles in the tank becomes 2282.5 cm3.

(a) Find the increase in water level of the tank in cm.
(b) A stick is 13cm long. If the stick just touches the water surface in the cube-shaped tank vertically, find the length of the stick that is exposed outside the tank.

Vol of water in tank : vol of pebbles and water = 3 : 5
3: 5 = V : 2300
V = 3/5 x 2300 = 1380
Base area of tank = 361
Hence water level = 1380/361 = 3.82cm

Is there missing information? Something must happen to cause an increase in the water level to solve (a), eg, the pail's water and pebbles poured into the cube??

Hi ksi, i've added the missing info... [/quote](a) When pebbles are added in , the volume of the pebbles will be the volume of water raised in the tank.
Volume of pebbles = 2282.5-1380 = 902.5
So level of water increase = 902.5/361 = 2.5cm

(b) Height of the tank = Sq root of 361 = 19 (because it is a cubic tank)
So if water is at 2.5+3.82= 6.32cm
19-6.32 = 12.68cm
So the length of stick exposed outside the tank would be 13-12.68=0.32cm.

[bobsg01]

In this answers, anyone can explain:


1) After - Kumar become 2 units

2) After - Lily become 5 units

How does the model detemine the After units for Kumar and Lily.

Thanks for your kind help. :scratchhead:

http://i52.tinypic.com/2na3f9h.jpg\">

[corneyAmber]

bobsg01:

In this answers, anyone can explain:


1) After - Kumar become 2 units

2) After - Lily become 5 units

How does the model detemine the After units for Kumar and Lily.

Thanks for your kind help. :scratchhead:

http://i52.tinypic.com/2na3f9h.jpg\">

Actually the \"after picture\" should not be drawn using the same scale as the \"before\" picture. The \"after\" picture is just trying to show that Lily is 2.5 times of Kumar and using the original scale to come up with 5 units and 2 units is misleading as we do not know after those changes, the proportion of the one unit remains the same. That is why you find it confusing. However, the ratio of 5 units to 2 units is correct in that it has to show Lily is 2.5 times of Kumar.

So in the equation, it makes no reference to the \"after\" model for the units. Simply put, it uses the units in the first model
Kumar -> 4 units - 325
Lily -> 3 units + 80
So to equate them to solve, 2.5 Kumar = Lily (the proportion shown in \"after\" where Lily ratio of Lily to Kumar is 5:2)

I would draw the diagram like this to make it clearer: (K' and L' means \"after\")
http://i55.tinypic.com/21myqt3.jpg\">

[MathIzzzFun]

bobsg01:

In this answers, anyone can explain:


1) After - Kumar become 2 units

2) After - Lily become 5 units

How does the model detemine the After units for Kumar and Lily.

Thanks for your kind help. :scratchhead:

http://i52.tinypic.com/2na3f9h.jpg\">

Hi bobsg01,

different sized blocks should be used for the \"before\" and \"after\" situations.

hope this helps

http://i56.tinypic.com/289zjis.jpg\">

cheers.

[bobsg01]

Thank you ksi and MathIzzzFun for the concise explanation.


http://i51.tinypic.com/mx08px.gif\">

[Hifive]

Hi


I refer to the PSLE exam questions booklet.
Need help on the solution provided :

why 12 / 0.8 ?

Pls refer to :
http://www.flickr.com/photos/62186744@N04/5915210246/

or is there an alternative method of solution?

Thanks in advance.

[MathIzzzFun]

Hifive:

Hi


I refer to the PSLE exam questions booklet.
Need help on the solution provided :

why 12 / 0.8 ?

Pls refer to :
http://www.flickr.com/photos/62186744@N04/5915210246/

or is there an alternative method of solution?

Thanks in advance.

Hi

Since Tap A and Tap B are flowing at the same rate, volume of water flowing into the respective tanks will be the same.

Ratio of increase in height in Tank A to that in Tank B
= 50 x 20 : 60 x 10
= 5 : 3
= 5u : 3u

Height in Tank B = 1/3 x 36 cm = 12 cm

So 2u = 12cm, 1u = 6cm.

The height of water level in both tanks will be 5u = 5 x 6cm = 30cm

Volume of water in Tank A = 30 cm x 60 cm x 10 cm = 18l
So, time taken = 18/1.2= 15 min.

cheers.

[stary]

Thanks ksi!!!

[Hifive]

Hi MathIzzzFun


Many thanks for your explanation to my question.

Cheers