the smallest of the three circles with center d has a radius of 8 inches and cb = ba = 4 inches. what is the…

Explanation:

Step1: Find the radii of the three circles

The radius of the smallest circle with center (D) is (r_1 = 8) inches. Since (CB=BA = 4) inches, the radius of the middle - sized circle (r_2=r_1 + CB=8 + 4=12) inches, and the radius of the largest circle (r_3=r_2+BA=12 + 4 = 16) inches.

Step2: Recall the formula for the area of a circle

The area of a circle is given by the formula (A=\pi r^{2}).

Step3: Calculate the areas of the three circles

The area of the smallest circle (A_1=\pi r_1^{2}=\pi\times8^{2}=64\pi) square inches. The area of the middle - sized circle (A_2=\pi r_2^{2}=\pi\times12^{2}=144\pi) square inches. The area of the largest circle (A_3=\pi r_3^{2}=\pi\times16^{2}=256\pi) square inches.

Step4: Calculate the sum of the areas

The sum of the areas of the three circles (A = A_1+A_2+A_3=64\pi+144\pi + 256\pi=(64 + 144+256)\pi=464\pi) square inches.

Answer:

(464\pi) in.(^{2})