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

Answer:

5.52 inch

Step-by-step explanation:

Recall :

Area of Sector : θ/ 360 * πr²

Sectors that do not allow movement : (8-3-2) = 3

Total sectors = 8

θ/ 360 = 3/8 ; Area = 35.9

Radius = r

35.9 = 3/8 * π * r²

35.9 / (3/8 * π) = r²

30.472866 = r²

r = √30.472866

r = 5.52 inch

The radius of the spinner is 5.520 inch whose  [tex]\frac{3}{8}[/tex]  sector area is 35.9 inches square.

It is given that the spinner used in a board game is divided into 8 equally sized sectors. three sectors indicate that the player should move his token forward on the board, two 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 and its area of the sector is 35.9 inches square.

It is required to find the radius of the spinner.

The region enclosed by the two radii of a circle and the arc is known as a sector's area. In other words sector area is a portion of the circle's area.

We know the formula of sector area (A):

[tex]\rm A= \frac{\theta}{360 \°} \pi r^2[/tex]    Where 'r' is the radius of the circle and [tex]\rm \theta[/tex] is in degree

The remaining sectors = ( Total sectors - Three sectors - Two sectors)

= ( 8 - 3 - 2) ⇒ 3 sectors indicate the player do not move his token

Total sector = 8

[tex]\rm \frac{\theta }{360 \° } = \frac{3}{8} \ when \ A = 35.9 \ inches^2[/tex]

Putting these values in the above formula, we get:

[tex]\rm 35.9 = \frac{3}{8} \pi r^2\\\rm 35.9\times 8 = 3\pi r^2\\\rm 287.2 = 3\pi r^2\\\\\rm \frac{287.2}{3} = \pi r^2\\\\\rm 95.733= \pi r^2\\\rm 30.4728 = r^2[/tex]Where [tex]\rm \pi[/tex] = 3.14159

[tex]\sqrt{30.4728} = r\\\rm 5.520= r \\\rm or = 5.520 \ inch[/tex]

Thus, the radius of the spinner is 5.520 inch.

Learn more about the area of sectors here:

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