Question

4. As shown in Figure 5.111 to the right if the

two small semicircles, each of radius 1 unit
with centres O' and O'' are contained in the
bigger semi-circle with center O, So that
O', O and O" are on the same line, then
what is the area of the shaded part?

Answer 1

Area of the shaded part is 3.14 square unit.

Explanation:

Area of the shaded part = Area of large semicircle - (Area of two small semi circles)

Area of large semicircle with center O =
`(1)/(2)(\pi r^2)`

=
`(1)/(2)\pi (2)^(2)`

= 2π

Area of semicircle with center O' =
`(1)/(2)\pi (1)^2`

=
`(\pi )/(2)`

Area of semicircle with center O" =
`(\pi )/(2)`

Now substitute these values in the formula,

Area of shaded part =
`2\pi - ((\pi )/(2)+(\pi )/(2))`

=
`\pi`

= 3.14 square unit

Area of the shaded part is 3.14 square unit.