Question

A point is chosen at random in the larger circle. What percent of the time will the point be in the shaded region? Round to the nearest tenth of a percent.
Please help me!!

Answer 1

Answer:

The dot will land on red 74.8% of the time

Step-by-step explanation:

To start off we need to find the Area of the whole circle. We can calculate this by using the Area of a Circle Formula on the larger circle measurement.

$A = \pi r^{2}$  .... A is Area, and r is radius.

$A = \pi 8.01^{2}$

$A = \pi *64.1601$

$Aw = 201.56in^{2}$ .... rounded to the nearest hundredth

So now we know that the area of the WHOLE circle is $201in^{2}$. Now we need to find the area of the inner white circle.

$Aw = \pi 4.02^{2}$

$Aw = \pi *16.1604$

$Aw = 50.77in^{2}$ .... rounded to the nearest hundredth

Now that we have the area of the whole circle and the area of the smaller inner circle we subtract them to find the area in red.

$Ar = 201.56in^{2} - 50.77in^{2}$

$Ar = 150.79in^{2}$

Lastly, we divide the Area in Red by the total Area to get the percentage of time the dot will land on red.

$d = \frac{150.79in^{2} }{201.56in^{2} }$

$d = 0.748 * 100$ .... multiply by 100 to turn decimal into a percent.

$d = 74.8$

Finally, we can see that the dot will land on red 74.8% of the time.

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