Question

A circle of diameter $20\text{ cm}$ is equally divided into five sectors. Find the area and perimeter of one of the sectors.

Hint:

Remember that the perimeter of a sector must include the two boundary radii!
Failing to add the $2r = 20\text{ cm}$ is a very common mistake.

Answer 1

Step 1: Find the radius.
Radius $r = \frac{20}{2} = 10\text{ cm}$.
Step 2: Work out the whole circle's area and circumference first.
Full circle area $= \pi r^2 = 3.14 \times 100 = 314\text{ cm}^2$. Full circumference $= 2\pi r = 2 \times 3.14 \times 10 = 62.8\text{ cm}$.
Step 3: Divide both by 5, since the circle is split into 5 equal sectors.
Area of one sector $= \frac{314}{5} = 62.8\text{ cm}^2$. Arc length of one sector $= \frac{62.8}{5} = 12.56\text{ cm}$.
Step 4: Add the two straight radii to get the perimeter.
Perimeter $= \text{arc length} + 2r = 12.56 + 20 = 32.56\text{ cm}$.
\[ \boxed{\text{Area} = 62.8\text{ cm}^2, \ \text{Perimeter} = 32.56\text{ cm}} \]