Question

Calculate the circumference of the circle.the length of the major arc. and the length of the minor arc to the nearest tenths

Answer 1

SOLUTION

The circle in the image has a radius r of 14m.

Let us label the major and minor arcs using the diagram below

Circumference of a circle is given as

$\begin{gathered} C\text{ = 2}\pi r \\ C\text{ = 2}\times3.14\times14 \\ C\text{ = 87.92} \\ C\text{ = 87.9m to the nearest tenths } \end{gathered}$

The length of the Major arc L1 will be

$\begin{gathered} \text{length of arc =}\frac{\theta}{360\text{ }}\times circumference\text{ of a circle } \\ \theta\text{ = is the angle of the arc } \\ \text{Length of major arc L1 = }\frac{300}{360\text{ }}\times87.92 \\ \\ L1\text{ = }\frac{5}{6\text{ }}\times87.92 \\ L1\text{ = 73.26666} \\ L1\text{ = 73.3 to the nearest tenths } \end{gathered}$

Length of minor arc L2 becomes

$\begin{gathered} L2\text{ = }\frac{60}{360\text{ }}\times87.92\text{ where the angle = 360 -300 = 60} \\ \\ L2\text{ = }\frac{1}{6}\times87.89 \\ L2\text{ = 14.65333} \\ L2\text{ = 14.7 to the nearest tenth} \end{gathered}$