The diagram consists of a large circle and four small circles.
Each of the smaller circles has radius 1 and touches the large circle and the two small circles next on either side of it.
To 3 significant figures, find the value of the shaded area in square units?
+129849 Join the centers of each of the small circles
This will create a square with a side of 2 and a diagonal of 2√2
The area of the square = 2^2 = 4 (1)
Then the diameter of the large circle = 2 + 2√2
So the radius = 1 + √2
So the area of the larger circle = pi (1 + √2)^2 = pi ( 3 + 2√2) (2)
And we will have 4 additional white areas that each have the area of 3/4 of a circle with a radius of 1
So.....the total of the areas = 4 (3/4) pi (1)^2 = 3 pi (3)
So....the grey area = (2) - (1) - (3) =
pi ( 3 + 2√2) - 4 - 3pi =
2√2 pi - 4 ≈
4.89 units^2 (rounded to 3 sig digits)
