A circle with radius of 3 cm sits inside a circle with radius of 5 cm. What is the area of the shaded region? Round your final answer to the nearest hundredth.

Hello!!

So first you need to find the area of the green circle. The formula for finding area for a circle is A = π r2. So the area for the green circle is 28.26 cm. Then you need to find the area of the blue circle. (Using the same formula) which would be 78.5. Then you subtract the value of the green circle to get the value of the shaded region which then your final answer is 50.24 cm. Hope this helped!!

About 50.24 cm^2 (Area of Shaded Region)

Step-by-step explanation:

Let's calculate the area of the shaded region by calculating the area of the bigger circle subtracted by the area of the smaller, nested circle:

The area of the bigger circle, given it's radius of 5 cm, can be calculated through the area formula πr^2. Now let's substitute, and, for simplicity, keep π as it is:

π (5 cm)^2 =

25π cm^2

Now the area of the smaller circle, given it's radius of 3 cm, can be calculated through the area formula πr^2 as done before. Again let us substitute, and, for simplicity, keep π as it is:

π (3 cm)^2 =

9π cm^2

To calculate the area of the shaded region, as discussed before, should be the difference between the larger and smaller circle's area as such:

25π cm^2 - 9πcm^2 =

16π cm^2

Now let's take π as 3.14 and calculate:

16(3.14) cm^2 =

Area of Shaded Region: 50.24 cm^2

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step-by-step explanation:

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1