Answer: (40/3)pi
This is the same as (40pi)/3
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Step-by-step explanation:
A = area of the smaller circle OB
A = pi*r^2
A = pi*3^2
A = 9pi
Circle OB has an exact area of 9pi square cm
We don't want the whole circle area, since we only are focusing on a 120 degree slice. Note how 120 degrees is 120/360 = 1/3 of a full circle; therefore we want 1/3 of the area to get the area of the slice
area of slice DOB = (1/3)*(area of circle OB)
area of slice DOB = (1/3)(9pi)
area of slice DOB = 3pi
We'll use this later so let's call this M
M = 3pi
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B = area of larger circle OA
B = pi*r^2
B = pi*7^2
B = 49pi
We take 1/3 of this for similar reasons as mentioned earlier. So the area of pizza slice COA is (1/3)*(49pi) = 49pi/3
We'll use this later so let N = 49pi/3
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Subtract the values of N and M.
Shaded area = N - M
Shaded area = (49pi/3) - (3pi)
Shaded area = (49pi/3) - (9pi/3)
Shaded area = (49/3)pi - (9/3)pi
Shaded area = (49/3 - 9/3)pi
Shaded area = (40/3)pi
side note: I think you computed 49/3 = 16.333 repeating which was the result for the area of circle OA; however it's not the final answer
another note: leave 40/3 as a fraction and don't convert it to 13.333 repeating. This is because the fraction 40/3 is exact while 13.333 is approximate