Question

Cups A and B are cone shaped and have heights of `12 cm` and `15 cm` and openings with radii of `6 cm` and `4 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

Cup A will not overflow and will fill up to a height of `6.67`.

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 `1/3pi6^2*12` = `(36*12)/3pi` = `144pi`
and volume of Cup B is `1/3pi4^(2)*15` = `(16*15)/3pi` = `80pi`.

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 `1/3pi6^2*a` = `80pi`

or `36a/3=80` or `a=80*3/36= 6.67` cm