Answer:
Hence the area of shaded region is 25.12 square inches.
Step-by-step explanation:
We are asked to find the area of the shaded region i.e. we need to find the area of the annulus region.
The radius of the inner circle(r) is [tex]\dfrac{7}{2}[/tex] inch.
and that of the outer circle(R) is [tex]\dfrac{9}{2}[/tex] inch.
since the diameter of the outer circle is 9 inch and hence its radius is [tex]\dfrac{9}{2}[/tex] inch.
similarly the radius of inner circle is: radius of outer circle-1 inch.
Hence the area of the shaded region is given by:
Area of the outer circle-Area of inner circle
Area of outer circle= [tex]\pi R^2[/tex]
and Area of inner circle= [tex]\pi r^2[/tex]
Hence the area of shaded region= [tex]\pi R^2-\pi r^2=\pi (R^2-r^2)[/tex]
[tex]=3.14\times ((\dfrac{9}{2})^2-(\dfrac{7}{2})^2)[/tex]
[tex]=3.14\times (\dfrac{81}{4}-\dfrac{49}{4})[/tex]
[tex]=3.14\times \dfrac{32}{4}[/tex]
[tex]=3.14\times 8\\\\=25.12[/tex]
Hence the area of shaded region is 25.12 square inches.
