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Question

In Fig. 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.

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Solution

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 shaded region=π×4.5222×π×1.522π×2.252+π×1.522

=π×4.522π×1.522π×2.252

=π2(20.252.25)π×5.0625

=π2(18)π×5.0625

=9ππ×5.0625

=π(95.0625)=3.9375π

Substitute~ π=227, we get,

Area of shaded region=3.9375×227=12.375

Therefore, area of the shaded region is 12.37 cm²

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

Cost=12.375×25=309.375 paise=Rs.3

Therefore, cost of painting the shaded region to the nearest rupee is rs 3.


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