Mathematics
In the figure, if the radius of each circle is 5 cm, then area of the shaded region is :
(400 - 50π) cm2
(400 + 100π) cm2
(400 - 100π) cm2
231 cm2
Mensuration
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Answer
There are 9 equal circles each with radius = 5 cm.The shaded region is the space between the four middle touching circles.
The centres of a the four middle circles form a square.
Diameter = 2r = 2 × 5 = 10 cm
Side of a square = 10 cm.
Area of square = (side)2
= 102 = 100 cm2.
Inside the square there are 4 quarter circles, which together to form one full circle of radius 5 cm.
∴ Area of circle = πr2
= π × 52 = 25π.
Area of one shaded region = 100 - 25π.
∴ For 4 identical shaded region
Total area = 4(100 - 25π)
= 400 - 100π cm2.
Hence, option 3 is the correct option.
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