SOLUTION: A cylindrical container A has radius 20 cm and height 25 cm. It is completely filled with water. A rectangular container B has length 40 cm and width 25 cm. Initially the contain

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Question 1120912: A cylindrical container A has radius 20 cm and height 25 cm. It is completely filled with water.
A rectangular container B has length 40 cm and width 25 cm. Initially the container B was empty.
All the water from container A is poured into container B.
The ration of the height of water to the height of container B is 2:3
Find the height of container B
Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!

VA = volume of cylinder (container A)
VA = pi*r^2*h
VA = pi*20^2*25
VA = pi*400*25
VA = 10000pi
VA = 10000*3.1415926535898
VA = 31415.926535898
which is approximate

VB = volume of rectangular prism or rectangular box (container B)
VB = L*W*H
VB = 40*25*H
VB = 1000*H
at this point, H is the unknown height of the box

All of the water in container A is poured into container B.
We have approximately 31415.926535898 cubic cm of water poured.
If VB were equal to this approximation, then we'd have some other height k such that

VB = 31415.926535898
1000*k = 31415.926535898
k = 31415.926535898/1000
k = 31.415926535898
The height of the water in container B is roughly 31.415926535898 cm.

We are told that the ratio of the height of water in container B to it's total height is 2:3.
What this means is that if the height of the water was say 2 cm, then the overall container would be 3 cm tall.

So we have this basic template
height ratio = (height of water)/(height of container)
turning into this
2/3 = k/H

Plug in the value for k. Solve for x
2/3 = k/H
2/3 = 31.415926535898/H
2*H = 3*31.415926535898
2*H = 94.247779607694
H = 94.247779607694/2
H = 47.123889803847

The approximate height of container B is roughly 47.12 cm.
This value has been rounded to two decimal places.
Round to further decimal places if you need more accuracy.