## anonymous one year ago The figure below shows a shaded circular region inside a larger circle: A shaded circle is shown inside another larger circle. The radius of the smaller circle is labeled as r and the radius of the larger circle is labeled as R. On the right side of the image is written r equal to 4 inches and below r equal to 4 inches is written R equal to 5 inches. What is the probability that a point chosen inside the larger circle is not in the shaded region?

1. anonymous

pic

2. anonymous

24% 36% 50% 64%

3. anonymous

one of these is answer ^

4. mathstudent55

You need to find what percentage of the large circle is the unshaded area. The unshaded region is the difference in the areas of the circles. First, find the areas of the two circles.

5. mathstudent55

Do you know hoe to find the area of a circle?

6. mathstudent55

Here is the formula: $$\large A_{circle} = \pi r^2$$

7. anonymous

so pi times 5?

8. mathstudent55

pi times 5 squared pi times 4 squared

9. mathstudent55

Remember the radius is squared in the formula for the area of a circle.

10. mathstudent55

This is how you find the areas of the circles: pi * 5 * 5 pi * 4 * 4

11. anonymous

so its 78.5 and 50.24?

12. anonymous

@mathstudent55 so its 78.5 and 50.24?

13. mathstudent55

Good. Now let's find the unshaded area. Subtract the smaller area form the larger area.

14. anonymous

@mathstudent55 so 28.26?

15. mathstudent55

Correct. Now you need to calculate what percentage of the large circle is the unshaded area.

16. mathstudent55

The unshaded area if the part. The large circle is the whole. To find what percent a part is of a whole, divide the part by the whole and multiply by 100.

17. anonymous

i dont get it :(

18. mathstudent55

Here is an example. Do you know that 50% means half?

19. anonymous

yeah

20. mathstudent55

Ok. Now I'm going to follow the rule above of finding a percent and show you how 50% means half. Since you already know that 50% means half, you'll understand this more easily. Then we can try the problem again.

21. mathstudent55

5 is half of 10. Since we know that 50% means half, we know that 5 is 50% of 10. What if we had to find what percentage of 10 is 5? We follow the rule above. 5 is the part. 10 is the whole. To find a percentage, divide the part by the whole and multiply by 100. 5/10 * 100 = 0.5 * 100 = 50 This shows us that 5 is 50% of 10.

22. mathstudent55

Here is a second example. We know that 25% is a quarter. 6 is a quarter of 24, so 6 must be 25% of 24. Let's calculate it to see how it's done. 6 is the part 24 is the whole 6/24 * 100 = 0.25 * 100 = 25 This shows that 6 is 25% of 24

23. anonymous

sorry i already finished it :P my brother answered it for me

24. mathstudent55

Now we can do the same with your problem. We have the unshaded area, 28.26. This is the part. The whole is 78.5. The percentage is: 28.26/78.5 * 100 = 36 The answer is 36%

25. mathstudent55

26. anonymous

yeah :P

27. anonymous

thanks anyway

28. mathstudent55

Great. If your brother can help you, that's great. It's easier to help if you're there than through a computer.

29. mathstudent55

You're welcome.