Aptitude - Volume and Surface Area - Discussion

12. 

A cistern of capacity 8000 litres measures externally 3.3 m by 2.6 m by 1.1 m and its walls are 5 cm thick. The thickness of the bottom is:

[A]. 90 cm
[B]. 1 dm
[C]. 1 m
[D]. 1.1 cm

Answer: Option B

Explanation:

Let the thickness of the bottom be x cm.

Then, [(330 - 10) x (260 - 10) x (110 - x)] = 8000 x 1000

320 x 250 x (110 - x) = 8000 x 1000

(110 - x) = 8000 x 1000 = 100
320 x 250

x = 10 cm = 1 dm.


Deepa said: (Jun 23, 2011)  
Please tell me why you subtracted by 10 in first step.

Priya Jain said: (Jul 26, 2011)  
@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

Ashish said: (Jan 17, 2012)  
How we can say 1.1m as bottom ? it is v=l*b*h.

Vani Varma said: (Feb 7, 2012)  
@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.....

Rahul said: (Mar 17, 2012)  
Why 8000 is multiplied by 1000?

Prasant said: (Mar 28, 2012)  
Ans to Rahul: 1 ltr = 1000 cc
Hence, 8000 ltr = 8000X1000 cc

Farri125 said: (Jul 7, 2013)  
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.

Efaz said: (Nov 28, 2013)  
Everything is clear expect that. Why didn't we substract 5cm from 110 cm (the height) , instead we took it as X?

Preetha said: (Apr 22, 2014)  
Still I didn't get that for what we are multiplying by 1000 with 8000?

Sahi said: (Jul 26, 2014)  
Volume is given in litres so we convert it into cubic cm by multiplying
it by 1000(because 1 liter = 1000 cubic cm).

Ujwala said: (Aug 17, 2014)  
Why to subtract thickness of both sides?

Deepak said: (Sep 18, 2014)  
Why length and breadth?

Why not just breadth and considering its radius?

Sharma said: (Sep 29, 2014)  
It's clearly given that thickness of the wall is 5cm.
Bottom part is not a wall, it is unknown, So consider X.

Thank You !

Tejas said: (Oct 4, 2014)  
What is 1 dm?

Tejaswini said: (Oct 10, 2014)  
dm in the sense diameter 10cm = 1dm.

Suriya said: (Dec 3, 2014)  
Hello sir if you want to find thickness of bottom. Why subtract 10 from the height instead of breath?

Mahesh said: (Jan 16, 2015)  
Why we are subtracting 10? Please tell any one.

Mani said: (Feb 7, 2015)  
I can't understand please tell me brief.

Sarwesh Alshi said: (May 16, 2015)  
Why not 2x? They wrote here only as x.

Sekar Agri said: (Jun 22, 2015)  
@Sarwash.

Thicknes of wall in length and breath, available both side. But in height, only bottom side thickness available.

Sikandar said: (Jun 23, 2015)  
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.

Mayawati Chotala said: (Feb 8, 2016)  
Still can't understand why 10? Which both sides are you talking about?

Pramod Kajla said: (May 26, 2016)  
@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).

Ramesh said: (Jul 5, 2016)  
Nothing I understand, please anyone explain in easy way.

Abhilasha said: (Aug 18, 2016)  
I am not getting this, Please explain this solution.

Narinder said: (Aug 19, 2016)  
@Tejaswini: 1 dm is Decimetre, not diameter.

Shanaya said: (Sep 24, 2016)  
Thank you so much @Vani Varma.

Manoj Kumar said: (Dec 30, 2016)  
@Pramod & @Narinder.

Well and correctly said.

Kin said: (Jan 15, 2017)  
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.

Twinkle Nagar said: (Feb 10, 2017)  
Our answer is 10 cm.

Then what is 1dm? Please, anybody tell me.

Rani Rajurkar said: (Mar 13, 2017)  
Why 8000 is multiplied by 1000 here?

Anil Kr said: (Jun 5, 2017)  
@Twinkle Nagar.

1dm means 1 decimeter.

Ramya said: (Jun 5, 2017)  
10^-2 is equal to cm same as 10^-1 is equal to decimeter.

Arshad said: (Jul 16, 2017)  
@Rani.

To convert it into cc.

Mr.Mp said: (Aug 26, 2017)  
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.

Shahir said: (Oct 2, 2017)  
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?

Maruf Bd said: (Feb 7, 2018)  
Please, Clear me that 1 dm= How many cm?

Shivani Agarwal said: (Mar 26, 2018)  
@Maruf Bd.

1 dm =10 cm.

Ashmita said: (May 4, 2018)  
Why we subtracted 10 here?

Jennier said: (Jul 3, 2018)  
How? I am not getting the solution.

Saru said: (Sep 28, 2018)  
I am not clear with subtracting 10 cm instead of 5 cm. Can anyone help me to getting this?

Onkar said: (Dec 5, 2018)  
Why subtracting 10cm?

Why not 5?

Rehan said: (Apr 5, 2019)  
@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?

Mahek said: (Jun 6, 2019)  
@Rehan.

They have given thickness of walls only not the bottom, so the thickness of the bottom may or may not be equal to the wall.

Akshau said: (Aug 12, 2019)  
dm means decameter.

10cm=1 decameter.

Rahul said: (Oct 7, 2021)  
How we get 10 multiples of each breadth depth and length? Please explain.

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