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

The radius is 9.28 inches.

Explanation:

Since there are 7 Move Ahead zones, and 3 Go Backwards zones on the spinner, there must be 2 other zones (the Freeze! +Bonus pts)

2 out of 12 zones are Freeze! +Bonus pts. That is 1/6 of the spinner. They said the area of the the Freeze!+Bonus pts is 45.1 inches squared.

45.1 × 6

= 270.6

The entire spinner has the area 270.6

The area of a circle is:

A = pi•r^2

We are looking for r. Thats the radius they asked for in the question.

270.6 = pi•r^2

pi is a number, I'm using the pi button on the calculator bc it is most exact.

270.6 = pi•r^2

Divide both sides by pi.

86.134655 = r^2

square root both sides.

9.28 = r

The radius is 9.28 inches.