Question

find the area of the sector in bold. Round the answer to the nearest 10th.

Answer 1

EXPLANATION:

We are given a circle with a major sector and a minor sector.

The major sector has a central angle measuring 315 degrees and a radius of 13km..

We are required to calculate the area of the sector in bold, that is, the MAJOR SECTOR.

First of all, the area of a sector is given by the formula;

$Area=\frac{\theta}{360}\times\pi r^2$

The variables here are;

$\begin{gathered} \theta=central\text{ }angle \\ r=13 \\ \pi=3.14 \end{gathered}$

We can now substitute the given values and calculate as follows;

$Area=\frac{315}{360}\times3.14\times13^2$$Area=\frac{7}{8}\times3.14\times169$$Area=464.3275$

Therefore, we round this to the nearest tenth and we'll have;

ANSWER:

$\begin{gathered} Area\text{ }of\text{ }sector\text{ }in\text{ }bold: \\ A=464.3km^2 \end{gathered}$