Question

The Length of an arc with central angle 40 degree in a circle is 8πcm What is the Length of an arc of Central angle 100degree in the same Circle?

Answer 1

length of arc = angle/360*2πr
OR
angle/180*πr
acc. to ques. 40/180*πr=8π
r=36cm

when angle is 100° , length of arc is:
=100/180*π*36
=20πcm

Answer 2

Given:-

• The Length of an arc with central angle 40° in a circle is 8π cm.

To Find:-

• Length of an arc of Central angle 100° in the same Circle.

Formula Used:-

• ${\boxed{\bf{Length\:of\:Arc=\dfrac{\theta}{360°}\times2\pi r}}}$

Solution:-

Firstly,

$\bf :\implies\:Length\:of\:Arc=\dfrac{\theta}{360°}\times2\pi r$

$\sf :\implies\:8\pi=\dfrac{40°}{360°}\times2\pi r$

$\sf :\implies\:8=\dfrac{1}{9}\times2\times r$

$\sf :\implies\:2r=9\times8$

$\sf :\implies\:r=\dfrac{72}{2}$

$\bf :\implies\:r=36\:cm$

Now, with Central Angle 100°:-

$\sf :\implies\:Length\:of\:Arc=\dfrac{100°}{360°}\times2\times \dfrac{22}{7}\times 36$

$\sf :\implies\:Length\:of\:Arc=\dfrac{10}{36}\times2\times \dfrac{22}{7}\times 36$

$\sf :\implies\:Length\:of\:Arc=10\times2\times \dfrac{22}{7}$

$\bf :\implies\:Length\:of\:Arc=\dfrac{440}{7}\:cm$

or,

$\bf :\implies\:Length\:of\:Arc=62.85\:cm$

Hence, The length of an arc of Central angle 100° in the same Circle is 440/7cm or 62.85cm.

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