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 96 208 464

Sum of areas of all the three circles is 464

Step-by-step explanation:

Given: Three concentric circles with center D.

Let C(D,r) be the smallest circle with radius r=CD=8 inches. r'=BD is radius of the middle circle C(D,r') and AB=r"=be the radius of the largest circle C(D,r").

Solution: Also, CB = BA=4 inches.

BD = BC + CD = 8+4 = 12 inches

AD = AB + BD =4 + 12= 16 inches

Now, we will calculate the areas of different circle separately.

Area of circle  C(D,r) = = 8*8* = 64      (1)

Area of circle  C(D,r') =   = 12*12* = 144       (2)

Area of circle  C(D,r'') =   = 16*16* = 256       (3)

Total area of all the three circles is  adding equation (1), (2),(3).

(64+144+256) =464