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...
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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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.
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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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