Question

Cups A and B are cone shaped and have heights of `32 cm` and `12 cm` and openings with radii of `5 cm` and `8 cm`, respectively. If cup B is full and its contents are poured into cup A, will cup A overflow? If not how high will cup A be filled?

Answer 1

When cup B is full and its contents are poured into cup A, cup A will not overflow. It will be filled up to a height of `30.72` cm

Explanation:

Volume of a cone whose radius is `r` and height is `h` is given by `1/3pir^2h`.

Hence volume of Cup A is `1/3pi5^2*32` = `(25*32)/3pi` = `800/3pi`
and volume of Cup B is `1/3pi8^(2)*12` = `(64*12)/3pi` = `768/3pi`.

As volume of Cup B is less than that of A, when cup B is full and its contents are poured into cup A, cup A will not overflow.

Let Cup A be filled till height `a`, than `1/3pi5^2*a` = `768/3pi`

or `25a=768` or `a=768/25= 30.72` cm