Question

find the area of the segments of a circle of radius 42 cm with central angle 120°.
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Answer 1

Segment => Segment is the area between arc and one cord except the radius ( which is longest cord )

$\bold{given \: \theta \: = 120 \degree}$

$\bold{radius = 42cm}$

Now we have to calculate the area if the segment so formed✓

So, the Formula to calculate the area of the segment is

$\red{ \bold{\frac{ \theta}{360} \times \pi \: r ^{2} - r ^{2} \times sin \frac{ \theta}{2} \times cos \frac{ \theta}{2}}}$

Let us calculate out

$= > \frac{120 \degree}{360 \degree} \times \frac{22}{7} \times 42 ^{2} - 42 ^{2} \times sin \frac{120 \degree}{2} \times cos \frac{120 \degree}{2} \\ \\ = > \frac{1}{3} \times 3.14 \times 1764 - 1764 \times sin60 \degree \times cos60 \degree \\ \\ = > \frac{5538.96}{3} - \frac{3055.33}{4} \\ \\ = > \frac{4 \times 5538.96 - 3 \times 3055.33}{12} \\ \\ = > \frac{22155.84 - 9165.99}{12} \\ \\ = > \frac{12989.85}{12} \\ \\ = > \red{ \huge{1082.48 \: cm ^{2} }}$

The area if the segment is 1082.48 cm²