Difference between revisions of "2021 AMC 12B Problems/Problem 6"
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+ | == Video Solution by OmegaLearn (3D Geometry - Cones and Cylinders) == | ||
+ | https://youtu.be/4JhZLAORb8c | ||
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+ | ~ pi_is_3.14 |
Revision as of 20:59, 11 February 2021
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