Circles in circule
If the radius of the big circle (and the big arcs) is what is the area of the yellow region in to one decimal place?
The answer is 7.3.
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1 solution
From the picture we see,
yellow area = big circle area - ( 2 * small circle area + 4 gray area)
to calculate the radius of small circle:
( R + r ) 2 = R 2 + ( R − r ) 2 , but R = 5
( 5 + r ) 2 = 5 2 + ( 5 − r ) 2
r = 1 . 2 5
area of small circle = 4.90873
to calculate the gray area:
b 2 = 2 5 − 6 . 2 5
b = 4 . 3 3
gray area = 1 2 0 / 3 6 0 ∗ 5 2 ∗ π − 4 . 3 3 ∗ 2 . 5
gray area = 2 6 . 1 7 9 9 − 1 0 . 8 2 5
gray area = 1 5 . 3 5 4 9
yellow area = 5 2 ∗ π − ( 2 ∗ 4 . 9 0 8 7 3 + 4 ∗ 1 5 . 3 5 4 9 )
yellow area = 7 . 3