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# A spinner used in a board game is divided into 8 equally sized sectors.

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A spinner used in a board game is divided into 8 equally sized sectors. Three of these sectors indicate that the player should move his token forward on the board, two 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 35.9 inches squared.

What is the radius of the spinner?

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

So far I have,

$$3/8( 360)= 135 degress$$

$$Area=1/2r^2sin135$$

$$35.9=1/2r^2(\sqrt 2/2)$$

Apr 3, 2020

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3 of the 8 sectors do not allow the player to move the token. This area is 35.9 in2.

(3/8)·pi·r2  =  35.9 in2

r  =  sqrt( 35.9 / pi · 8/3 )

Apr 3, 2020