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Question: "In the figure below, both circles have the same center, and the radius of the larger circle is R. If the radius of the smaller circle is 3 units less than R, which of the following represents the area of the shaded region?"

Answer IS: (pi)R^2-(pi)(R-3)^2

*Can someone explain how? I don't even know how to start. ~will draw diagram under~

Question: In the figure below, both circles have the same center, and the radius of the larger circle is R. If the radius of the smaller circle is 3 units less class=

Verified Answer :

diene

The formula for the area of a circle is πr^2, where r is the radius of the circle.
The area of your figure is (outer circle)-(inner circle)
plugging in R and R-3 for radii:
the area of the shaded region is (pi)R^2-(pi)(R-3)^2
hope this helped!

JeanaShupp

Answer: \(\pi\ R^2-\pi\ (R-3)^2\)


Step-by-step explanation:

Given : Two circles centered at the same center

Radius of the larger circle = R units

Radius of smaller circle= R-3 units

We know that area of circle with radius 'r' is \(\pi\ r^2\)

Area of the larger circle=\(\pi\ R^2\)

Area of the smaller circle =\(\pi\ (R-3)^2\)

Therefore, the area of the shaded region

=Area of the larger circle-Area of the smaller circle

=\(\pi\ R^2-\pi\ (R-3)^2\)

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