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In the figure below, a wheel with center O rolls, without slipping, in a straight line across a level floor. Two spots of wet paint at points A and B on the rim of the wheel leave marks on the floor, as indicated by the dots on the floor. What is the value of x ? ( Note:X is degrees) X is the degree measure of the arc.
7 in | 8 in | 7 in | circle
7 in | 8 in | 7 in | circle
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02 Aug 2003, 13:25
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I've never seen this before used in geometry. 
But, I think I got your idea, Stolyar.
15 inches 7 inches
----------- = ---------
360 degrees x how many degrees in a circle
X= 168.
Let me try to upload the picture. 15 inches should represent a diameter.
The x represents a portion of the degree measure of the semi-circle arc or the diameter
The diameter is 30 inches and represents half the degree measure in a circle. 22 inches so far taken up.
x = 11
--- ----
180 15
168 degrees / 180 degrees or 11/15 of the circumference of the semi-circle is rolled.
Arc Measure = 11/15 * 2 pi r= 30
Arc Measure = 22
The line segment length of 22 corresponds to 11/15 of the circle's circumference. This makes it a classic GMAT Problem.
But, I think I got your idea, Stolyar.
15 inches 7 inches
----------- = ---------
360 degrees x how many degrees in a circle
X= 168.
Let me try to upload the picture. 15 inches should represent a diameter.
The x represents a portion of the degree measure of the semi-circle arc or the diameter
The diameter is 30 inches and represents half the degree measure in a circle. 22 inches so far taken up.
x = 11
--- ----
180 15
168 degrees / 180 degrees or 11/15 of the circumference of the semi-circle is rolled.
Arc Measure = 11/15 * 2 pi r= 30
Arc Measure = 22
The line segment length of 22 corresponds to 11/15 of the circle's circumference. This makes it a classic GMAT Problem.
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
