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प्रश्न
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.
उत्तर
(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`
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