Aptitude - Volume and Surface Area - Discussion


A boat having a length 3 m and breadth 2 m is floating on a lake. The boat sinks by 1 cm when a man gets on it. The mass of the man is:

[A]. 12 kg
[B]. 60 kg
[C]. 72 kg
[D]. 96 kg

Answer: Option B


Volume of water displaced = (3 x 2 x 0.01) m3
= 0.06 m3.

Mass of man = Volume of water displaced x Density of water
= (0.06 x 1000) kg
= 60 kg.

Haritha said: (Aug 3, 2011)  
Why did we take volume of water displaced here?

Suraj said: (Aug 18, 2011)  
From where 0. 01 comes?

Thenmozhi said: (Sep 13, 2011)  
How density of water calculated ?

Gurpreet said: (Oct 21, 2011)  
Why did we take volume of water displaced here?

How density of water calculated?

Ramanathan said: (Dec 21, 2011)  
When an object is immersed in water the volume of water displaced by the object is not equal to the mass of object. It is equal to the volume of object. In this case the volume of man is 0.06 cubic meters. We should know the density of man to calculate the mass of man, not density of water.

Mrinal said: (Feb 21, 2012)  
The height is given 1cm when it sinks, so H is 0.01m.

Hannan said: (Jan 13, 2013)  
How density of water is measured? Can anybody help me please.

Svk said: (Jan 27, 2013)  

Density of H2O IS 1000kg/m3.
Google density of water and it gives you 1000kg/m3.

Sabha said: (Mar 2, 2013)  
Density of water always 1000kg/m3.

Raju Subba said: (Apr 15, 2014)  
How is the density of water calculated?

Aashritha said: (Feb 28, 2015)  
What is the formula used in calculating the volume of water displaced l*b*h, If so?

Moses said: (Apr 17, 2015)  
Guys, remember from the question, the man sat on the boat and the boat was floating meaning that his weight is equal to the weight of the fluid displaced (Archimedes principle).

But Density = Mass/Volume. Make mass the subject you get.

Mass of water displaced = Volume of water displaced x Density of water.

So from the above explanation, Mass of the man = Mass of water displaced.

Hence Mass of man = Volume of water displaced x Density of water.

Ashish said: (Aug 18, 2015)  
Simple density is mass per unit vol.

Density of water is 1000 kg/m^3 is always CONSTANT.

Volume is calculated from given parameters l*b*h.

Therefore density = (mass/volume).

Mass = (density*volume).

Mass = (1000/(l*b*h)).

Ans = 1000*0.06.

Suhaas said: (May 1, 2016)  
How volume of water displaced is equal to the mass of a man?

Aliza Mir said: (Jul 31, 2016)  
@Suhaas, via the Archimedes principle.

Varun said: (Nov 23, 2016)  
How volume of water is taken as l*b*h?

Latha said: (Dec 10, 2016)  
It is solved by using Archimedes principle.

Mihir Jha said: (Feb 24, 2017)  
Hi friends, we can do this sum by applying the concept of buoyancy.
Increase in weight =Inc in buoyant force.
Therefore,Mg = vdg,
M = vd,
M = (2 * 3 * 0.01)m * 1000,

(Vol. Of water displaced * density of water).
Thus mass of the man is 60 kg.

Kapil said: (Mar 22, 2017)  
Why not the mass is 72kg?

Skd said: (Dec 29, 2017)  
Please define 0.01 where it comes from?

Priya said: (Mar 13, 2018)  
By using the concept of buoyancy I couldn't understand.

Please help me, @Mihir Jha.

Harsha said: (Feb 24, 2019)  

1cm = 0.01m.

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