Given:
A larger circle consisting of two circles with radii of 4 cm and 8 cm each.
To find:
The area of the shaded region.
Solution:
The centers of the circles with radii 4 cm and 8 cm lie on the same line as the center of the larger circle.
So the diameter of the outer circle [tex]= 8+8+4+4=24[/tex] cm.
If the diameter is 24 cm, the radius is [tex]\frac{24}{2} =12[/tex] cm.
The area of the shaded region is obtained by subtracting the areas of the two inner circles from the outer circle.
The area of a circle [tex]= \pi r^{2} .[/tex]
The area of the circle with radius 12 cm [tex]= \pi (12^{2}) = 3.14(144) = 452.16[/tex] square cm.
The area of the circle with radius 8 cm [tex]= \pi (8^{2}) = 3.14(64) = 200.96[/tex] square cm.
The area of the circle with radius 4 cm [tex]= \pi (4^{2}) = 3.14(16) = 50.24[/tex] square cm.
The area of the shaded region [tex]= 452.16-200.96-50.24 = 200.96[/tex] square cm.
Rounding this off to the nearest tenth, we get the area of the shaded region as 201 square cm.
