A cylindrical bucket 28cm in diameter and 72cm high is full of water .The water is emptied into a rectangular tank 66cm long and 28cm wide.Find the height of the water level in the tank.
Answer
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Hint: We use the concept of “law of conservation of mass” , considering density to be constant of water and thus equating their volume in a cylindrical bucket and after the water is emptied to the rectangular tank.
Complete step-by-step answer:
In the above question we will equate the volume of cylindrical bucket and rectangular tank.
As, we already know that;
Volume of cylindrical bucket = πr2h, where, r= radius and h= height.
And, the volume of the cuboid(rectangular tank) = \[l\times b\times h\] , where, l= length,b= width and h= height.
Now,we have; r=\[\dfrac{diameter}{2}\] =28/2=14cm and h=72cm.
So,the volume of the cylindrical bucket= \[\pi \times {{14}^{2}}\times 72c{{m}^{3}}\].
Again,for the rectangular tank we have;
l=66cm ,b=28cm and h= height of water level= ?
So, the volume = \[(66\times 28\times h)c{{m}^{3}}\].
Now, we will equate the volume and we get;
\[\pi \times {{14}^{2}}\times 72c{{m}^{3}}\]= \[(66\times 28\times h)c{{m}^{3}}\]
On, further simplification we will get;
$\Rightarrow h=\dfrac{\pi \times {{14}^{2}}\times 72}{66\times 28}cm$
On calculating the above we get;
h= 24cm
Hence, the answer of the above question will be 24cm.
Therefore, the height of the water level in the tank will be 24cm.
NOTE:
Remember the concept that in the above type question we always use the concept of equating volume under the condition mentioned above. Also, be careful during the calculation and don’t use the value of π as 3.14 anywhere until it’s not mentioned.
Complete step-by-step answer:
In the above question we will equate the volume of cylindrical bucket and rectangular tank.
As, we already know that;
Volume of cylindrical bucket = πr2h, where, r= radius and h= height.
And, the volume of the cuboid(rectangular tank) = \[l\times b\times h\] , where, l= length,b= width and h= height.
Now,we have; r=\[\dfrac{diameter}{2}\] =28/2=14cm and h=72cm.
So,the volume of the cylindrical bucket= \[\pi \times {{14}^{2}}\times 72c{{m}^{3}}\].
Again,for the rectangular tank we have;
l=66cm ,b=28cm and h= height of water level= ?
So, the volume = \[(66\times 28\times h)c{{m}^{3}}\].
Now, we will equate the volume and we get;
\[\pi \times {{14}^{2}}\times 72c{{m}^{3}}\]= \[(66\times 28\times h)c{{m}^{3}}\]
On, further simplification we will get;
$\Rightarrow h=\dfrac{\pi \times {{14}^{2}}\times 72}{66\times 28}cm$
On calculating the above we get;
h= 24cm
Hence, the answer of the above question will be 24cm.
Therefore, the height of the water level in the tank will be 24cm.
NOTE:
Remember the concept that in the above type question we always use the concept of equating volume under the condition mentioned above. Also, be careful during the calculation and don’t use the value of π as 3.14 anywhere until it’s not mentioned.
Last updated date: 14th Sep 2023
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