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? 80πin.² 96πin.² 208πin.² 464πin.²

Explanation:

Step1: Find the radius of each circle

• For the smallest circle: radius \(r_1 = 8\) inches.
• For the middle - sized circle: \(r_2=8 + 4=12\) inches.
• For the largest circle: \(r_3=8 + 4+4 = 16\) inches.

Step2: Use the formula for the area of a circle \(A=\pi r^{2}\)

• Area of the smallest circle \(A_1=\pi\times8^{2}=\pi\times64 = 64\pi\)
• Area of the middle - sized circle \(A_2=\pi\times12^{2}=\pi\times144 = 144\pi\)
• Area of the largest circle \(A_3=\pi\times16^{2}=\pi\times256=256\pi\)

Step3: Calculate the sum of the areas

\(A = A_1+A_2+A_3=64\pi+144\pi + 256\pi=(64 + 144+256)\pi=464\pi\)

Answer:

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