Question

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?

Answer 1

Cone A will overflow because it has a volume 1052.434`cm^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.