Question

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

Answer 1

Diameter $=35mm$
$\therefore$ Circumference of circle

$=2\times \pi \times r$ $=2\times \pi \times 17.5=110mm$

i) The total length of the silver wire required
$=$ Circumference of circle $+$ $(5\times 35)$
$=110+175$ $=$ $285mm$
(ii) The area of each sector of the brooch
$=\frac{\text{Area of circle}}{10}$
$=\frac{\pi \times 17.5\times 17.5}{10}$
$=\frac{385}{4}{mm}^2$