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?
O
80 rt in.
O
96 te in.?
O
20811 in.2
464rt in.

The sum of the areas of all three circles is 464 squared inches, if the smallest of the three circles with center D has a radius of 8 inches and  CB = BA = 4 inches.

Step-by-step explanation:

The given is,

                Three circles,

                Smallest circle with center D has a radius of 8 inches.

                CB = BA = 4 inches

Step:1

               Ref the attachment,

               Radius of smallest circle(DC) = 8 inches

               Radius of middles circle (DB),

                           DB = BC + DC = 4 + 8 = 12 inches

               Radius of largest circle (DA),

                              DA = AB + BC + CD = 4 + 4 + 8

                                                         DA = 16 inches

Step:2

               Formula for area of circle,

                             .............................(1)

               Where, r - Radius of circle

               Area of smallest circle,

                                r = 8 inches

              Equation (1) becomes,

                            =

                                       = 64

                            = 64 squared inches

             Area of middle circle,

                                r = 12 inches

              Equation (1) becomes,

                            =

                                         = 144

                              = 144 squared inches

              Area of Largest circle,

                                r = 16 inches

              Equation (1) becomes,

                            =

                                         = 256

                            = 256 squared inches

Step:3

             Sum of area of three circles  = Area of small circle

                                          + Area of middle circle + Area of larger circle

                                                              = 64 +  144 + 256

                                                             = 464 squared inches

Result:

           The sum of the areas of all three circles is 464 squared inches, if the smallest of the three circles with center D has a radius of 8 inches and  CB = BA = 4 inches.

(-5,-28)

i graphed to on desmos.