Cups A and B are cone shaped and have heights of 24 cm and 21 cm and openings with radii of 8 cm and 11 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
Jan 9, 2018

Cone A will overflow because it has a volume 1052.434cm^3 lower than Cone B.

Explanation:

First, find the volume of both cones using the equation V = pir^2h/3
V - Volume
r - radius
h - height

Cone A - V = pi(8)^2(24)/3 ~~ 1608.495cm^3
Cone B - V = pi(11)^2(21)/3 ~~ 2660.929cm^3

Cone B has a greater volume. Therefore, Cone A will overflow in the scenario presented.