Question

the area of the circular ring in terms of theradius of the inner circle, x, which is 2 unitsless than the radius of the outer circle?

Answer 1

Answer:

The area of the circular ring in terms of the radius of the inner circle, x is;

$A=4\pi(x+1)$

Explanation:

Area of the circular ring is equal to the area of the outer circle minus the area of the inner circle.

let x represent the radius of the inner circle.

The inner circle radius is 2 unit less than the raduis of the outer circle;

$R=x+2$

Area oof a circle can be written as;

$A=\pi r^2$

where r is the radius'

So, the area of the circular ring is;

$\begin{gathered} A=A_1-A_2 \\ A=\pi R^2-\pi x^2 \\ \end{gathered}$

substituting R;

$\begin{gathered} A=\pi R^2-\pi x^2 \\ A=\pi(x+2)^2-\pi x^2 \\ A=\pi(x^2+4x+4)-\pi x^2 \\ A=\pi(x^2+4x+4-x^2) \\ A=\pi(4x+4) \\ A=4\pi(x+1) \end{gathered}$

Therefore, the area of the circular ring in terms of the radius of the inner circle, x is;

$A=4\pi(x+1)$