Question

Cups A and B are cone shaped and have heights of `29 cm` and `28 cm` and openings with radii of `7 cm` and `12 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

Since `V_B > V_B`, cup A will overflow.

Explanation:

Formula for volume of a cone is given by `V = (1/3) pi r^2 h`

`r_A = 7cm, h_A = 29cm, r_B = 12 cm, h_B = 28cm`

`V_A = (1/3) pi 7^2 * 29 = 1488.07` `cm^3`

`V_B = (1/3) pi 12^2 * 28 = 4222.3` `cm^3`

Since `V_B > V_B`, cup A will overflow.