Question

A spinner used in a board game is divided into 12 equally sized sectors. Seven of these sectors indicate that the player should move his token forward on the board, three of these sectors indicate that the player should move his token backward, and the remaining sectors award the player bonus points but do not move his token on the board.
The total area of the sectors that do not allow the player to move his token is 45.1 inches squared.

What is the radius of the spinner?

Enter your answer, rounded to the nearest tenth of an inch, in the box.

Answer 1

Answer:

20.8 inches squared

Step-by-step explanation:

Area of spinner:

45.1 is the area of sectors where the token doesn't move, which 5 sectors doesn't move the token (don't forget that the bonus points doesn't move token). Then

45.1/5=9.02

9.02*12=108.24

K=1/2(r^2)sin150

108.24=1/2(r^2)sin150

216.48=(r^2)1/2

432.96=r^2

r=20.8