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

Calculate The Circumference Of The Circlethe Length Of The Major Arc And The Length Of The Minor Arc To The Nearest Tenths class=

Sagot :

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

[tex]\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}[/tex]

The length of the Major arc L1 will be

[tex]\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}[/tex]

Length of minor arc L2 becomes

[tex]\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}[/tex]

View image DarekK707051
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