Question

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.

37(i) What is the radius of the circle?

Hint:

Keep the radius in fraction form ($\frac{35}{2}$) because it will make calculations in the following parts much simpler, allowing terms to easily cancel out with $\pi = \frac{22}{7}$.

Answer 1

Step 1: Recall what a diameter and a radius mean.
The diameter of a circle is the longest chord, passing through the centre and touching the circle at both ends. The radius is exactly half this length, since the centre sits at the midpoint of any diameter.

Step 2: Apply this relationship to the brooch.
We are told the wire forms a circle of diameter $35\text{ cm}$. Being half of this diameter, the radius is
\[ r = \frac{35}{2}\text{ cm} = 17.5\text{ cm} \]
Final Answer:
The radius of the circle is $17.5\text{ cm}$ (or $\frac{35}{2}\text{ cm}$). \[ \boxed{17.5\text{ cm}} \]