How to Find the Percentage of Area Outside a Square Inscribed in a Semicircle?

In summary, the problem is to find the percentage of the area of the circle that is outside of the inscribed square. A helpful hint is to draw lines from the center of the circle to where the square meets the circle, which will lead to a solution. If needed, more assistance can be provided by discussing attempted solutions.
  • #1
Kyupuccino
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0

Homework Statement



A square of maximum area is inscribed in a semicircle as shown. What percent (rounded to the nearest tenth) of the area of the circle is outside the square?

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Homework Equations





The Attempt at a Solution



I'm so desperately lost, someone, please help me! :'(

It would be greatly appreciated if you could!
 
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  • #2
Hint: draw some dotted lines from the center of the circle to the points where the square meets the circle.

Once you do that, you will probably be able to figure out what to do. If you can't, work on it for a bit and then tell us what you've tried and we'll have more help for you.
 

Related to How to Find the Percentage of Area Outside a Square Inscribed in a Semicircle?

1. What is a square of maximum area?

A square of maximum area is a square with the largest possible area, given a specific constraint or set of constraints.

2. How do you find the maximum area of a square?

To find the maximum area of a square, you can use the formula A = s^2, where A is the area and s is the length of one of the sides. Set the derivative of this formula equal to 0 and solve for s to get the maximum value.

3. What is the significance of finding the maximum area of a square?

Finding the maximum area of a square is important in many real-world applications, such as maximizing the use of space in a room or minimizing the amount of material needed for a project.

4. Are there any constraints for finding the maximum area of a square?

Yes, there can be constraints depending on the specific problem. For example, the square may need to fit within a certain space or have a specific perimeter.

5. Can the maximum area of a square be found using different methods?

Yes, there are various methods for finding the maximum area of a square, such as using calculus, geometry, or even trial and error. The most efficient method will depend on the specific problem and constraints.

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