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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 than class=

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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: [tex]\pi\ R^2-\pi\ (R-3)^2[/tex]


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 [tex]\pi\ r^2[/tex]

Area of the larger circle=[tex]\pi\ R^2[/tex]

Area of the smaller circle =[tex]\pi\ (R-3)^2[/tex]

Therefore, the area of the shaded region

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

=[tex]\pi\ R^2-\pi\ (R-3)^2[/tex]

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