What is the area of each sector of the brooch?

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Solution

Q.
A brooch is crafted from silver wire in the shape of a circle with a diameter of 35 mm. The wire is also used to create 5 diameters, dividing the circle into 10 equal sectors, as shown in the figure.

Based on the above information, answer the following questions:

(iii) (b) What is the area of each sector of the brooch

1 $96.25 {mm}^{2}$

2 $86.25 {mm}^{2}$

3 $94.25 {mm}^{2}$

4 $93.25 {mm}^{2}$

Ans.
(1)

Angle subtended by arc at each sector $= \frac{360 °}{10} = 36 °$

∴ Area of each sector $= \frac{36 °}{360 °} \times π \times {(\frac{35}{2})}^{2} = \frac{1}{10} \times \frac{22}{7} \times \frac{35}{2} \times \frac{35}{2} = 96.25 {mm}^{2}$

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