How much did the level of cider in the pot go down?

Question

You have some apple cider in a cylindrical pot that has a radius of 4inches. You pour cider from the pot into a cup that has a radius of 1.5 inches. until the cider in the cup is 4 in. deep. How much did the level of cider in the pot go down?

Answer 1

V=∏r^2h

V=∏(1.5^2)(4)

V=∏(2.25)(4)

V=∏(9) for the cup

 

for the pot the height does not matter, so let the height be 5 inches (or whatever height you like)

V=∏(4^2)(5)

V=∏(16)(5)

V=∏(80) for the pot

 

V=80∏-9∏

V=71∏ left in the cup

now find the height of the pot and compare it with the original height

 

71∏=∏(4^2)h

71∏=16∏h

divide both sides by ∏

71=16h

h=71/16

h=4 7/16 inches

the original height was 5 inches

 5-4 7/16=9/16 of an inch

the level went down 9/16 of an inch in the pot

Answer 2

Hi Sara,

 

First, you need to know the formula for volume of a cylinder which is pi times the square of the radius times the height of the column. 

 

Then calculate the volume of the cup.

 

Then calculate the amount that the level of the pot went down by plugging in the volume of the cup and the radius of the pot.

 

So. . . cup volume = pi x 1.5^2 x 4 = 28.27 cubic inches

 

Now for the pot:  28.27 = pi x 4^2 x height lost

 

28.27/16pi = height

 

height = 0.56 inches.  This makes sense because a cylinder with a larger radius will have a smaller height compared to an equal volume in a cylinder with a smaller radius.  You can try this yourself using drinking glasses with different radii.

 

Have fun.

 

Dan