Question

In the following figure, there are three semicircles, A, B and C having diameter 3 cm each, and another semicircle E having a circle D with diameter 4.5 cm are shown. Calculate:

(i) the area of the shaded region

(ii)  the cost of painting the shaded region at the rate of 25 paise per cm² , to the nearest rupee.

 

Answer 1

(i) Area of the shaded region can be calculated as shown below,

Area of the shaded region = Area of the semi-circle with diameter of 9 cm − area of 2 semi-circles with radius 3cm − area of the circle with centre D + area of semi-circle with radius 3 cm

`∴ "Area of the shaded region "=(pixx4.5xx4.5)/2-(2xxpixx1.5xx1.5)/2-pixx2.25xx2.25+(pixx1.5xx1.5)/2`

`"rea of the shaded region"= (pixx4.5xx4.5)/2-(pixx1.5xx1.5)/2-pixx2.25xx2.25`

`∴ "Area of the shaded region " pi/2(20.25-2.25)-pixx5.0625`

`∴"  Area of the shaded region"=pi/2(18)-pixx5.0625 `

`∴"  Area of the shaded region"=9pi-pixx5.0625`

`∴"  Area of the shaded region"=pi(9-5.0625)`

`∴"  Area of the shaded region"=3.9375 pi`

Substituting `pi=22/7 "we get"`

`∴"  Area of the shaded region"=3.9375xx222/7`

`∴"  Area of the shaded region"=12.375`

Therefore, area of the shaded region is`12.375 cm^2`

Now we will find the cost of painting the shaded region at the rate of 25 paise per cm². 

`∴ "Cost" =12.375xx25`

`∴ "Cost"=309.375`  paise 

`∴ "Cost"=Rs=3`

Therefore, cost of painting the shaded region to the nearest rupee is Rs `3`