Question

What is the approximate area of the shaded region in square inches? Use π = 3.14.

Answer 1

Hence the area of shaded region is 25.12 square inches.

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
`(7)/(2)` inch.

and that of the outer circle(R) is
`(9)/(2)` inch.

since the diameter of the outer circle is 9 inch and hence its radius is
`(9)/(2)` 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=
`\pi R^2`

and Area of inner circle=
`\pi r^2`

Hence the area of shaded region=
`\pi R^2-\pi r^2=\pi (R^2-r^2)`

`=3.14* (((9)/(2))^2-((7)/(2))^2)`

`=3.14* ((81)/(4)-(49)/(4))`

`=3.14* (32)/(4)`

`=3.14* 8\\\\=25.12`

Hence the area of shaded region is 25.12 square inches.