Question

the smallest of the three circles with center d has a radius of 8 inches and
cb = ba = 4 inches.
what is the sum of the areas of all three circles?
$80\pi$ in.$^{2}$
$96\pi$ in.$^{2}$
$208\pi$ in.$^{2}$
$464\pi$ in.$^{2}$

Explanation:

Step1: Find radius of smallest circle

The smallest circle has radius $r_1 = 8$ inches (DC = 8 in).

Step2: Find radius of middle circle

Middle circle radius: $r_2 = DC + CB = 8 + 4 = 12$ inches.

Step3: Find radius of largest circle

Largest circle radius: $r_3 = DC + CB + BA = 8 + 4 + 4 = 16$ inches.

Step4: Calculate area of each circle

Area formula: $A = \pi r^2$
Smallest area: $\pi (8)^2 = 64\pi$
Middle area: $\pi (12)^2 = 144\pi$
Largest area: $\pi (16)^2 = 256\pi$

Step5: Sum the three areas

Total area: $64\pi + 144\pi + 256\pi = 464\pi$

Answer:

464π in.²