"Published in Newark, California, USA"
A wooden ball 11.15 in. in diameter sinks to a depth of 9.37 in. in water. Find the area of the wet surface.
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
A spherical zone or zone, in short is a portion of the surface of a sphere from its circular cross section to its end (for one base) or between two parallel circular planes (for two bases). The above figure is a zone of one base.
In this problem, we will solve for the area of spherical zone of one base. Since we want to solve for the area of the wooden ball at the wet surface, then we have to solve for the area of the spherical zone of one base at the bottom part. The area of the spherical zone of one base is given by the formula
Substitute the values of R and H to the above equation, we have
Therefore,
or
