"Published in Newark, California, USA"
A pine log 40 ft. long has a uniform circular cross section of radius 11 in. The ends lie in parallel planes which are not perpendicular to the axis of the log. How much paint will be required to give the log (ends not included) two coats, if 1 gal. of paint covers 800 sq. ft. of surface? If pine weighs 31 lbs. per cu. ft., find the weight of the log.
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 surface or lateral area of a circular cylinder which is a pine log is
where pk is the circumference or perimeter of the cross section and e is the length of an element or the slant height. Substitute the values, we have
Therefore, the amount of paint required to paint the surface of a pine logs in two coats is
The volume of a circular cylinder which is a pine log is
where K is the area of a cross section and e is the length of an element or the slant height. Substitute the values, we have
Therefore, the weight of a pine log is
