How should the radius MP be drawn?

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In summary, the conversation discusses finding the radius of MP in order to divide the coloured space into two parts with equal areas. The suggested method is to find a formula for the area of both parts and solve for the position of P that makes the areas equal. However, it is mentioned that this does not require any integration and can be solved by finding the area of the left part using the formula for the area of a circle.
  • #1
Dafoe
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I need help with this one.

http://g.imagehost.org/view/0971/24_p_181


The coloured parts space is limited by three semicircle archs of which the smaller has the radius r.

How should the radius MP be drawn, if you want it to divide the coloured space into two parts with
equally big areas?
 
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  • #2
What have you tried? Where are you stuck? At first glance, it would look like the most obvious thing would work:

1. Find a convenient way to quantify the position of P
2. Compute a formula for the area of the left blue part
3. Compute a formula for the area of the right blue part
4. Solve for the position of P that makes those areas equal
 
  • #3
This doesn't require any integration at all. If you draw a vertical downward from M, you cut the blue region into two parts. The area of the left part is 1/4 the area of the large circle plus 1/2 the area of the small circle. What is that?
 

1. What is the purpose of drawing the radius MP?

The radius MP is drawn to accurately measure the distance from the center of a circle to any point on its circumference. This measurement is important in various mathematical and scientific calculations.

2. How do you determine the length of radius MP?

The length of radius MP can be determined by using the formula r = c/2π, where r represents the radius and c represents the circumference of the circle. Alternatively, it can also be measured using a ruler or compass.

3. Should the radius MP be drawn from the center of the circle?

Yes, the radius MP should always be drawn from the center of the circle to any point on its circumference. This ensures that the measurement is accurate and consistent.

4. Can the radius MP be drawn in any direction?

No, the radius MP should always be drawn in a straight line from the center of the circle to the desired point on its circumference. Drawing it in any other direction would result in an incorrect measurement.

5. Is it necessary to draw the radius MP if the circle is already labeled with its diameter?

Yes, it is still important to draw the radius MP even if the circle is already labeled with its diameter. The radius is a crucial measurement in many mathematical and scientific calculations, and it is always better to have multiple points of reference for accuracy.

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