Question

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?

Answer 1

pic

Answer 2

24%
36%
50%
64%

Answer 3

one of these is answer ^

Answer 4

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.

Answer 5

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

Answer 6

Here is the formula:

\(\large A_{circle} = \pi r^2\)

Answer 7

so pi times 5?

Answer 8

pi times 5 squared
pi times 4 squared

Answer 9

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

Answer 10

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

Answer 11

so its 78.5 and 50.24?

Answer 12

@mathstudent55 so its 78.5 and 50.24?

Answer 13

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

Answer 14

@mathstudent55 so 28.26?

Answer 15

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

Answer 16

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.

Answer 17

i dont get it :(

Answer 18

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

Answer 19

yeah

Answer 20

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.

Answer 21

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.

Answer 22

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

Answer 23

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

Answer 24

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%

Answer 25

Did your brorther get 36%?

Answer 26

yeah :P

Answer 27

thanks anyway

Answer 28

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

Answer 29

You're welcome.