Calculate the rise in the level of water when a brick with a volume of 1500cu.cm is immersed in water

Question

A cylindrical can has an internal radius of 20cm stand upright on a flat surface. It contains water to a depth of 20 cm. please step by step and explain a bit. Thank you it's highly appreciated you help others on here!! 

Answer 1

First let's calculate the total volume of the water in the can.  The formula is πr²h, where r is the radius and h is the height (or depth).

 

So that gives us a total volume of π*20²*20 = 8000π cm³ (cubic centimeters).

 

So now let's add in the brick.  That's going to increase the total volume of "stuff" in the can by 1500 cm³.  So now the total volume is 8000π + 1500.

 

Now adding a brick is pretty much the same as adding water with the same volume.  Adding the brick will push up the water around it, and adding water will basically do the same thing.  So think of this can as having 8000π + 1500 cm³ of water.  Let's write an equation that describes this:

 

V = πr²h

 

Since the radius is still 20, this becomes:

 

V = 400πh

 

Set this equal to 8000π + 1500, which is the new volume:

 

400πh = 8000π + 1500

 

Now solve for h:

 

h = (8000π + 1500) / 400π

h = (80π + 15) / 4π