Aptitude - Volume and Surface Area - Discussion

Consider fish tank on a flat surface, with very strong side glasses which is 5cm thick and the bottom glass thickness, is not given we have to find it. The fish comes out to measure his house length from OUTSIDE it notes that it is 3.3 m or 330cm in length, Now if the fish measured from inside it would get 10 cm less than 330 because the thickness 5+5 in two sides does not come into the picture. similarly, breadth, when measured outside it, was 260 cm from inside 10 cm less which is 250 . Height 110 cm from outside but bottom glass thickness is not known we have to find it let it be x which is 110-X ( Height of its house is small so it was able to jump outside LOL). Now amount of water, that is a volume that fits inside the tank is 8000 liters but we need it in cubic not in liters so for conversion multiply by 1000.

(Think if the glass walls were very thick said 8cm or more, then the volume of water would have fitted less than 8000 liters.). Always if we have the length, breadth and height measured from outside and volume is given and the walls have a certain thickness. we cannot directly apply l,b, h in the volume formula. if the question thickness is negligible then directly you can apply in the formula.

320+250+110-X=8000*1000.
X=10cm answer is in cm as we have converted l,b,h to cm.
Now centi is 10 power -2 which is 1/100 and deci is 10 power -1 which is 1/10
10 cm is nothing but 10 * 10 ^ -2 m = 10/100 which is nothing but 0.1
1dm is nothing but 1*10^-1 m =1/10 nothing but 0.1.

Note : mili = 10^-3= 1/1000, deci = 10^-1=1/10 , micro =10^-6= 1/1000000, centi=10^-2=1/100.

so 8000*1000= 320+250+ 110-X.

@All.

Here is the explanation for all who are not getting why 10 is subtracted.

3.3m = 330cm, which is the length of the rectangular opposite faces of the cistern. Now the wall is present on both (opposite) sides whose thickness is 5cm.
So internal length (which is being calculated to compare with capacity) will be 330-5-5 cm
Similarly for internal breadth, external breadth - thickness of both opposite walls, that is, 260cm - 5cm(thickness of 1st wall) - 5cm(thickness of the opposite wall).

So, internal breadth = 260 - 5 - 5.

The bottom thickness isn't given so we considered it as x.

Also, there's no information about the top face, so we don't have to take its thickness into consideration(negligible) or assume that the cistern is open.

In the question, it has given that the cistern has the capacity of 8000 litres, which means that the internal volume of the cistern is 8000 litres.
And he has given the thickness of the side walls but not the thickness of the bottom (we have to calculate).
The external side length, breadth, depth as 330cm, 260cm, 110cm. To get internal sides we have to subtract the thickness from external sides. Hence length=330- (2*5) (since we have to consider both sides of the walls).
i.e. l=320cm, b=250cm, d=110-x (since only one bottom is there).

Finally, we have to equal these two volumes to get the required thickness of the bottom.

@All.

For the better understanding of this question, you have to visualize in 3D (like a cuboid with walls and open at top), then only you will be able to understand the actual concept of question.

Because for inner length and breadth, the thickness will be used from two sides (considerr it as left and right), but for height it will be calculated from one side (consider it as bottom side only), because the cuboidal tank is open from upside (as there will be the four sides of wall and one will be bottom).

@ashish.........
3.3 , 2.6 and 1.1 are the length breadth and depth of the cistern respectively..

1.1 is the total depth of the cistern including its thickness....

and the thickness at bottom is vat we need to find out.....

@deepa
The thickness is given as 5 cm and the dimensions given are external dimensions so in order to get internal dimension we subract the external dimensions by thichness on both sides so 5*2=10

In Question Where he asked to find the thickness of internal?

And Thickness of any object isn't equal to internal thickness? if not so prove, with logical reasoning with example. Thanks.

@All.

When they mention the thickness of walls as 5 cm, it can also mean the bottom, isn't it?

The bottom can also have the same thickness in that sense, right?

On the Left-hand side, we have.

320*250*(110-x) which are all in cm so its cm cube.
while on Right-hand side, we have
8000 * 1000 m cube?

Why is that?

How from the question it is clear that whether it is open at top or not because in solution it is consider only bottom thickness while subtraction.