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A brooch is crafted from silver wire in the shape of a circle with a diameter of $35$ cm. The wire is also used to create $5$ diameters, dividing the circle into $10$ equal sectors as shown in figure.
Based on the above information, answer the following questions :
(i) What is the radius of circle ?
(ii) What is the circumference of the brooch?
(iii) (a) What is the total length of silver wire required ?
OR
(iii) (b) What is the area of each sector of the brooch?
Based on the above information, answer the following questions :
(i) What is the radius of circle ?
(ii) What is the circumference of the brooch?
(iii) (a) What is the total length of silver wire required ?
OR
(iii) (b) What is the area of each sector of the brooch?
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(i) $r = \frac{35}{2}$ cm $= 17.5$ cm (I) (1 Mark)
(ii) Circumference $= 2 \times \frac{22}{7} \times \frac{35}{2} = 110$ cm (I) (1 Mark)
(iii) (a) Total length of wire required $= (5 \times 35 + 110)$ cm (I) (1 Mark)
$= 285$ cm (II) (1 Mark)
OR
(iii) (b) Central angle of each sector $= \frac{360}{10} = 36^\circ$ (I) (1 Mark)
Area of each sector $= \frac{36}{360} \times \frac{22}{7} \times \frac{35}{2} \times \frac{35}{2}$
$= \frac{385}{4}$ or $96.25$ cm$^2$ (II) (1 Mark)
(ii) Circumference $= 2 \times \frac{22}{7} \times \frac{35}{2} = 110$ cm (I) (1 Mark)
(iii) (a) Total length of wire required $= (5 \times 35 + 110)$ cm (I) (1 Mark)
$= 285$ cm (II) (1 Mark)
OR
(iii) (b) Central angle of each sector $= \frac{360}{10} = 36^\circ$ (I) (1 Mark)
Area of each sector $= \frac{36}{360} \times \frac{22}{7} \times \frac{35}{2} \times \frac{35}{2}$
$= \frac{385}{4}$ or $96.25$ cm$^2$ (II) (1 Mark)