Question 205404
The plan is to find the area of each circle and then subtract the smaller area from the larger area to get the area of the annulus.
The two circles are defined by:
{{{(x+2)^2+(y-6)^2 = 16}}} and...
{{{(x+2)^2+(y-6)^2 = 81}}}
Comparing these with the general form of the equation of a circle with center at (h, k) and radius, r:
{{{(x-h)^2+(y-k)^2 = r^2}}} you can immediately read off the square of the radius of each circle as {{{r[1]^2 = 16}}} and {{{r[2]^2 = 81}}} respectively.
The area of each circle is given by:
{{{A[1] = pi*r[1]^2}}} and...
{{{A[2] = pi*r[2]^2}}} so you have...
{{{A[1] = pi*(16)}}} and...
{{{A[2] = pi*(81)}}} Subtracting {{{A[2] - A[1]}}} you get:
{{{pi*(81)-pi*(16) = highlight(pi*65)}}}={{{highlight(204.2)}}}sq.units. (Approx.)