Question

The radius of the bull’s-eye of the dartboard is 8 inches. The radius of each concentric circle is 8 inches more than the radius of the circle inside it. If a dart lands at random on the dartboard, what is the probability that the dart will hit in area C?
A. 9/16
B. 5/16
C. 1/4
D. 3/4

Answer 1

Answer with Step-by-step explanation:

The radius of the bull’s-eye of the dartboard is 8 inches.

The radius of each concentric circle is 8 inches more than the radius of the circle inside it.

Radius of first circle=8 in.

Radius of second circle=16 in.

Radius of third circle=24 in.

Radius of fourth circle=32 in.

Area of C=Area of the third circle-Area of second circle

                     = π×24×24-π×16×16

                   = 320π sq. in.

Total area of dartboard=Area of fourth circle=π×32×32

                                                            =1024π sq. in.

P( the dart will hit in area C)= area of c/total area of dart board

                                             =320π/1024π

                                           =  5/16

Hence, correct option is:

B.5/16