"Published in Newark, California, USA"
A vertical stone column 12.5 ft. high has an elliptical base with the longer axis twice the shorter. If the weight of the column is 12,400 lbs. and if the stone weighs 160 lbs. per cu. ft., find the area of the largest and smallest axial section of the column.
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 |
The area of the ellipse which is the base of the column is
but
Hence, the above equation becomes
The volume of the column which is a cylinder is
The length of b which is the semi-minor axis of the ellipse is
The length of a which is the semi-major axis of the ellipse is
Therefore, the area of the largest axial section of the column which is a rectangle is
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| Photo by Math Principles in Everyday Life |
and the area of the smallest axial section of the column which is a rectangle is
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| Photo by Math Principles in Everyday Life |
