Question

A brooch is made with silver wire in the form of a circle with diameter 35 mm. The wire is also used in making 5 diameters which divide the circle into 10 equal sectors as shown in figure. Find the total length of wire required and the area of each sector. [3 MARKS]

Answer 1

Concept: 1 Mark
Application: 2 Marks

The length of the wire used for making the circumference
$=\pi d=\pi \times 35=109.96mm$

The length of wire used for making 5 diameters
$=5d=5\times 35=175mm$.

Total length of wire required
$=175+109.96=284.96mm$

Since 5 diameters are made, the angle in each sector
$=\frac{360}{10}={36}^{\circ }$

Area of each sector
$=\frac{36}{360}\times \pi \times {17.5}^2$

$=96.16m{m}^2$