Question

The diagram shows a sector of a circle radius 10cm. Find the perimeter of the sector, giving your answer correct to 1 decimal place

Answer 1

Explanation:

Hello! Remember you have to write complete questions in order to get good and exact answers. Anyway, I'll help you either way. A sector is a region of a circle between two radii. Let's assume the sector as:

$s=25\pi cm^2$

Then, we can find the central angle by the following equation:

$s=\frac{\theta}{360}\times\pi r^{2} \\ \\ r=10cm \\ \\ s=25\pi cm^2 \\ \\ \\ So: \\ \\ \frac{25\pi(360)}{10^2\pi}=\theta \\ \\ \theta = 90^{\circ}$

But:

$90^{\circ}=\frac{\pi}{2}$

Then:

$C:Perimeter \ of \ sector \\ \\ \\ C=\theta r \\ \\ C=\frac{\pi}{2}(10) \\ \\ C=5\pi cm \approx \boxed{15.7cm}$