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
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.
Related Questions
Four circular cardboard pieces, each of radius 7 cm are placed in such a way that each piece touches two other pieces. The area of the space enclosed by the four pieces is :
42 cm2
40 cm2
21 cm2
18 cm2
If sum of the areas of two circles with radii r1 and r2 is equal to the area of circle of radius r, then :
r = r1 + r2
r > r1 + r2
r2 < r12 + r22
r2 = r12 + r22