"Published in Newark, California, USA"
Two balls, one 6 in. in diameter and the other 4 in. in diameter are placed in a cylindrical jar 9 in. in diameter, as shown. Find the volume of water necessary to cover them.
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| Photo by Math Principles in Everyday Life |
Solution:
The first that we have to do is to analyze and label the given figure as follows
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| Photo by Math Principles in Everyday Life |
Consider a right triangle between the centers of two spheres and use Pythagorean Theorem in order to solve for x as follows
The height of a right circular cylinder is
The volume of a right circular cylinder is
The volume of a big sphere is
The volume of a small sphere is
Therefore, the volume of water necessary to cover the two balls is
or you can give the value of pi as follows
