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A brooch is made with silver wire in the form of a circle with a diameter of 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in the fig. Find:
(i) The total length of the silver wire required
(ii) The arc of each sector of the brooch.

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\frac{35}{4} m m^{2}

\frac{85}{4} m m^{2}

\frac{385}{4} m m^{2}

None

answer is C.

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Detailed Solution

Given,
Diameter = 35 mm.
Circumference of circle,

= 2 \times π \times r

= 2 \times π \times 17.5

= 110 mm

Total length of the wire of silver needed,
= Circumference of circle

+ (5 \times 35)

= 110 + 175

= 285 mm

Each sector area of the brooch,

= \frac{Area of circle}{10}

= \frac{π \times 17.5 \times 7.5}{10}

= \frac{385}{4} m m^{2}

Option 3 is correct.

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