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?

1 Answer
Apr 17, 2018

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.
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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.