Question

The smallest of the three circles with center D has a radius

Answer 1

The sum of the areas of all three circles is 464$\pi$ 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,

                             $A = \pi r^{2}$.............................(1)

               Where, r - Radius of circle

               Area of smallest circle,

                                r = 8 inches

              Equation (1) becomes,

                            $A_{small}$ = $\pi (8)^{2}$

                                       = 64$\pi$

                            $A_{small}$ = 64$\pi$ squared inches

             Area of middle circle,

                                r = 12 inches

              Equation (1) becomes,

                            $A_{middle}$ = $\pi (12)^{2}$

                                         = 144$\pi$

                             $A_{middle}$ = 144$\pi$ squared inches

              Area of Largest circle,

                                r = 16 inches

              Equation (1) becomes,

                            $A_{largest}$ = $\pi (16)^{2}$

                                         = 256$\pi$

                           $A_{Larger}$ = 256$\pi$ squared inches

Step:3

             Sum of area of three circles  = Area of small circle

                                          + Area of middle circle + Area of larger circle

                                                              = 64$\pi$ +  144$\pi$ + 256$\pi$

                                                             = 464$\pi$ squared inches

Result:

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

Answer 2

Answer:

464 $\pi$ $in.^{2}$

Step-by-step explanation:

did it on edge