2021 AMC 12B Problems/Problem 6
Problem
An inverted cone with base radius and height
is full of water. The water is poured into a tall cylinder whose horizontal base has radius of
. What is the height in centimeters of the water in the cylinder?
Solution
The volume of a cone is where
is the base radius and
is the height. The water completely fills up the cone so the volume of the water is
.
The volume of a cylinder is so the volume of the water in the cylinder would be
.
We can equate these two expressions because the water volume stays the same like this . We get
and
.
So the answer is
--abhinavg0627
Video Solution by OmegaLearn (3D Geometry - Cones and Cylinders)
~ pi_is_3.14