Question

Find the length of the arc in a circle with radius 4 cm and an arc subtends an

angle 90° at the centre.
​

Answer 1

GiveN :-

• Radius of circle = 4 cm

• Value of ∅ = 90°

To FinD :-

• Length of the arc

SolutioN :-

Length of arc is :

$:\implies \boxed{ \blue{ \bf Arc = 2\pi r \times \frac{ \theta}{360} }} \\ \\:\implies \sf Arc = 2 \times \frac{22}{7} \times 4 \times \frac{90}{360} \\ \\:\implies \sf Arc = 2 \times \frac{22}{7} \times \cancel 4 \times \frac{1}{ \cancel4} \\ \\:\implies \sf Arc = \frac{44}{7} \\ \\ :\implies \boxed{ \sf Arc = 6.28 \: cm}$

Answer 2

$❥ᴀ᭄ɴsᴡᴇʀ$

Area of sector OAPB =

$πr^2θ/360$

$= 22/7 \: \times \: 10 \times 10 \times 90/360$

$550/7$

Area of major sector = area of circle - area of sector OAPB

$=πr^2−550 /7$

$=22 /7×10×10−550 /7$

$=2200 /7−550 /7$

$=1650 /7 \: cm^2$

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