Mathematics
Grade9
Easy

Question

If angle angle B O X is 120 degree, what is the area of sector BOX in square meters? (radius = 15 m)

  1. 225pi    
  2. 115pi    
  3. 15pi    
  4. 75pi    

hintHint:


Area of the sectorequals fraction numerator A n g l e   o f   sec invisible function application t o r over denominator 360 to the power of 0 end exponent end fraction cross times   pi r to the power of 2 end exponent

The correct answer is: 75pi


    To find the area of a sector, simply multiply the total area of the circle by the fraction of the part you are looking at.
    In this case, our area will come from the following:
    A equals pi r to the power of 2 end exponent equals pi cross times left parenthesis 15 m right parenthesis to the power of 2 end exponent equals 225 pi m to the power of 2 end exponent
    To find the fractional part of the circle we care about, take the number of degrees in angle B O X over the total number of degrees in a circle 360 to the power of ring operator end exponent ):
    fraction numerator 120 over denominator 360 end fraction equals fraction numerator 1 over denominator 3 end fraction
    So, we find our answer by multiplying these two parts together:
    225 pi m to the power of 2 end exponent cross times fraction numerator 1 over denominator 3 end fraction equals 75 pi m to the power of 2 end exponent

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