A two dimensional picture of a circular onion ring is shown at the right. The inner radius of the onion ring is x cm. and the thickness of the ring is 1 cm. Which of the numbered choices represents the area, in square centimeters, of the onion ring (the shaded region)?
1) 2)
3) 4)
1) (2X+1)*pi
2) 2*pi
3) 2x*pi
4) pi
done, see your other post
To find the area of the onion ring, we need to subtract the area of the inner circle from the area of the outer circle.
The area of a circle is given by the formula A = πr^2, where A is the area and r is the radius.
The inner circle has a radius of x cm, so its area is A_inner = πx^2.
The outer circle has a radius of (x + 1) cm, so its area is A_outer = π(x + 1)^2.
To find the area of the onion ring, we need to subtract the area of the inner circle from the area of the outer circle.
A_ring = A_outer - A_inner
= π(x + 1)^2 - πx^2
= π(x^2 + 2x + 1) - πx^2
= πx^2 + 2πx + π - πx^2
= 2πx + π
So, the area of the onion ring is 2πx + π square centimeters.
Now, let's look at the numbered choices:
1) 2)
3) 4)
We can see that none of the choices is in the form of 2πx + π. Therefore, none of the choices represents the correct area of the onion ring.