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Home > PC > Chapter 6 > Lesson 6.4.1 > Problem 6-147


Two logs of radius cm and cm have a single wire around them as shown in the figure below. Find the length of the wire. Hint: and are right angles. Draw a line through parallel to meeting at .

Larger circle on left labeled, a, with point on top labeled, c, & smaller circle on right labeled, b, with point on top labeled, d, circles are tangent to each other. Dashed segments from, a, to, c, & from, b, to, d, are parallel radii, & segments from, c, to, d, & 2 unlabeled points on bottom of each circle, each segment tangent to both circles

Label the drawing!

Line because it is the sum of the radii of both logs.

Segment added from center A to Center B, point added on radius, A C, dividing it into 2 sections, inner section labeled 60, outer section labeled 20, line through new point & center point Bm with radius, B D, labeled 20, angles A C D, & B D C each labeled 90 degrees, angle, C A B labeled theta.

Then , so radians. Thus the wire length around the large log is cm.