Area of the shaded regions is [tex]13\frac{1}{3}\pi[/tex] square cm.
What is area of a circle?
"Area of a circle is the region occupied by the circle in a two-dimensional plane. It can be determined easily using a formula, A = [tex]\pi r^{2}[/tex], where r is the radius of the circle. The unit of area is the square unit, such as square meter, square centimeter, etc."
We have
Inner circle radius = 3cm
Outer circle radius = 4 + 3 cm = 7cm
Formula to find the area of circle
A = [tex]\pi r^{2}[/tex]
Area of inner circle
A = [tex]\pi. 3^{2}[/tex]
⇒ A = [tex]9\pi[/tex]
Since, [tex]120^{0}[/tex] is [tex]\frac{1}{3} of 360^{0}[/tex]
Thus, it means the shaded area of the figure is of [tex]\frac{1}{3}[/tex] of the circle.
∴ A = [tex]\frac{9\pi }{3}[/tex]
⇒ A = [tex]3\pi[/tex] square cm
Area of outer circle
A = [tex]\pi. 7^{2}[/tex]
⇒ A = [tex]49\pi[/tex]
Since, it means the shaded area of the figure is of [tex]\frac{1}{3}[/tex] of the circle.
∴ A = [tex]\frac{49\pi }{3}[/tex] square cm
Area of the shaded regions = Area of outer circle - Area of inner circle
A = [tex]\frac{49\pi }{3}-3\pi[/tex]
⇒ A = [tex]\frac{49\pi-9\pi }{3}[/tex]
⇒ A = [tex]\frac{40\pi }{3}[/tex]
⇒ A = [tex]13\frac{1}{3}\pi[/tex] square cm
Hence, Area of the shaded regions is [tex]13\frac{1}{3}\pi[/tex] square cm.
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