Question

Cups A and B are cone shaped and have heights of `35 cm` and `29 cm` and openings with radii of `14 cm` and `9 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

`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.

Explanation:

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