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?

Guest May 22, 2020

#1**+2 **

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)

CPhill May 22, 2020