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Question -

A brooch is madewith silver wire in the form of a circle with diameter 35 mm. The wire is alsoused in making 5 diameters which divide the circle into 10 equal sectors asshown in Fig. 12.12. Find:

(i) the total lengthof the silver wire required.

(ii) the area ofeach sector of the brooch.



Answer -

 Find:

(i) the total lengthof the silver wire required.

(ii) the area ofeach sector of the brooch.

Diameter (D) = 35 mm

Total number of diameters to be considered= 5

Now, the total length of 5 diameters thatwould be required = 35×5 = 175

Circumference of the circle = 2πr

Or, C = πD = 22/7×35 = 110

Area of the circle = πr2

Or, A = (22/7)×(35/2)2 =1925/2 mm2

(i) Total length of silver wire required = Circumference ofthe circle + Length of 5 diameter

= 110+175 = 185 mm

(ii) Total Number of sectors in the brooch = 10

So, the area of each sector = total area ofthe circle/number of sectors

Area of each sector = (1925/2)×1/10 = 385/4 mm2

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