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.
Last updated date: 16th Mar 2023
•
Total views: 303.6k
•
Views today: 3.85k
Answer
303.6k+ views
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.
Recently Updated Pages
If a spring has a period T and is cut into the n equal class 11 physics CBSE

A planet moves around the sun in nearly circular orbit class 11 physics CBSE

In any triangle AB2 BC4 CA3 and D is the midpoint of class 11 maths JEE_Main

In a Delta ABC 2asin dfracAB+C2 is equal to IIT Screening class 11 maths JEE_Main

If in aDelta ABCangle A 45circ angle C 60circ then class 11 maths JEE_Main

If in a triangle rmABC side a sqrt 3 + 1rmcm and angle class 11 maths JEE_Main

Trending doubts
Difference Between Plant Cell and Animal Cell

Write an application to the principal requesting five class 10 english CBSE

Ray optics is valid when characteristic dimensions class 12 physics CBSE

Give 10 examples for herbs , shrubs , climbers , creepers

Write the 6 fundamental rights of India and explain in detail

Write a letter to the principal requesting him to grant class 10 english CBSE

List out three methods of soil conservation

Fill in the blanks A 1 lakh ten thousand B 1 million class 9 maths CBSE

Epipetalous and syngenesious stamens occur in aSolanaceae class 11 biology CBSE
