If a dart board is divided into twenty equal sectors and the diameter of the board is 18 inches, what area of the board does each sector cover?If a dart board is divided into twenty equal sectors...

If a dart board is divided into twenty equal sectors and the diameter of the board is 18 inches, what area of the board does each sector cover?

If a dart board is divided into twenty equal sectors and the diameter of the board is 18 inches, what area of the board does each sector cover?

 

The dart board is a circle.

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The circular dart board has a diameter of 18 inches. So, its radius is 18/2 = 9 inches.

Therefore its area is pi*r^2 = pi*9^2

This is divided into 20 equal sectors.

So the area of each sector is pi*81/20 = 12.72 square inch approximately.

neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

Posted on

Area A of the circle is given by the formula:

A = pir^2.

The diameter of the dart board = 18 inches.

So the radius of the dart board = diameter/r = 18/2  = 9inch.

So the area of the circular dart board = pi*r^2 = pi*9^2. = 81pi sq inches.

Since board is covered in 20 equal sectors, the area covered in each sector = A/20 = Pir^2/20 = 81pi/20  = 4.05pi sq inches = 12.7235 sq inch nearly.

The area covered in each of 20 equal sectors = 4.05pi sq in, or 12.7235 sq in.

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