posted by jakkie j on .
a can of soup completely fills a cylinder 5 inches tall and 3 inches in diameter. If one can of soup is poured into a cylindrical pot with a diameter of 6 inches, to what depth, in inches, will it fill the pot?
is the answer 10?
If you think about it, that won't work logically. Your 2nd pot is wider than your first pot, so it will have to be more shallow to fill the same amount of water.
V= pi x r^2 x h
So the first thing we have to do is figure out the volume of the first cylinder.
Pi = 3.14
The radius is half the diameter. So 1/2 of 3 is 1.5. 1.5 squared is 2.25 inches.
The height is 5 inches.
3.14 x 2.25 x 5
That's 35.325 inch^3
That's how much water we have. Now, we just have to plug that into the same equation for the 2nd thing.
35.325 = 3.14 x 9 x ?
35.325 = 28.26x
So take 35.325 divided by 28.26 and your answer is...
With twice the diameter, the base area is 4 times that of the small, full can. That means the liquid inside the wider can will rise to 1/4 the former height, or 5/4 inch.
This agrees with the previous answer but is easier to calculate.