SOLUTION: 1. Find the area of the shaded segment of a circle with radius 10cm and central angle 45 degree. ----------- ----------- ---- 2. Solve the pro

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Question 319945: 1. Find the area of the shaded segment of a circle with radius 10cm and central angle 45 degree.
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2. Solve the proportion:

Show that the answer is

Found 2 solutions by stanbon, Edwin McCravy:
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
The Question:find the area of the shaded segment of a circle with radius 10cm and central angle 45 degree.
h:10=1:root 2
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Equation:
h/10 = 1/sqrt(2)
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h = 10/sqrt(2)
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h = 10sqrt(2)/2
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h = (10/2)sqrt(2)
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h=5 root 2
My Question: how do you get 1 after the equal sign?
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The "1" is the numerator of the right side of the equation.
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Cheers,
Stan H.
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Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!

1. Find the area of the shaded segment of a circle with radius 10cm and central angle 45 degree.

That's the red area below:


The area of the sector A is to 45° as the area of the whole circle is to 360°:

The area of a whole circle is 



So





Cross-multiply:



Divide both sides by 360







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2. Solve the proportion:





Cross-multiply:





Divide both sides by 



Cancel on the left:





Rationalize the denominator on the right side by multiplying it by 







Edwin
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