Question

Cups A and B are cone shaped and have heights of `20 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

Since volume of cup B (2412.7432) > volume of cup A (523.5988), #excess quantity of 1889.1444 cc from Cone B will overflow.

Explanation:

Volume of a cone `V = (1/3) pi r^2 h`

Given : `r_a = 5 cm, r_b = 8 cm, h_a = 20 cm, h_b = 12 cm`

`V_a = (1/3) * pi * 5^2 * 20 = 523.5988` `cc`

`V_b = (1/3) * pi * 8^2 * 12 = 2412.7432` `cc`

Since volume of cup B (2412.7432) > volume of cup A (523.5988), #excess quantity of 1889.1444 cc from Cone B will overflow.