Question

Cups A and B are cone shaped and have heights of `24 cm` and `21 cm` and openings with radii of `8 cm` and `15 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 B has `3` times more volume, so Cup A will overflow.

Explanation:

`V = 1/3 * pi * r^2 * h` Calculate the two volumes. If B is greater than A, it will overflow. If it is less, use the volume calculated to find the equivalent height of A.

`V_A = 1/3 * pi * r_A^2 * h_a`
`V_B = 1/3 * pi * r_B^2 * h_b`

`V_A = 1/3 * pi * 8^2 * 24` ; `V_A = 1608.5`
`V_B = 1/3 * pi * 15^2 * 21` ; `V_B = 4948.0`

Cup B has `3` times more volume, so Cup A will overflow.