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How much drink?



We have a cylindrical glass, which can hold 12 ounces of liquid. It is 6 inches tall. It is tipped so that my drink is about to spill out the top. The liquid is 2 inches from the bottom, on the other side (See the diagram). How many ounces of liquid are still in the glass?


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It's 2/3 full, so there's 8 oz in the glass.

The volume subtended by parallel planes displaced axially by 2" does not depend on the angle the planes make with the axis. The rest of the liquid is equal in volume to the empty space, by symmetry. Each of the three mentioned volumes are thus 1/3 of the capacity of the glass.
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Volume of Cylinder= pi x r^2 x h = 12 ounce

So pi x r^2 = 2 (Note: h = 6")
Considering half cone of height 4" and cylinder of height 2", the volume of liquid comes to

1/2[1/3 x pi x 4r^2 x 4"] + pi x r^2 x 2"
Putting the value of pi x r^2 as 2
Volume of liquid = 28/3
So 28/3 ounce is the answer.

Edited by bhramarraj
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