Question

13. Find the area of the sector of a circle of radius 7cm ,if corresponding arc length is 6.2cm.
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Answer 1

Answer:

s = rθ, so

a = 1/2 r^2 θ = 1/2 * 49 * (6.2/7) = 21.7

Answer 2

$\boxed {\underline {\mathbb {FINAL\:ANSWER:-}}}$

$\boxed {area\:of\:circle\: \implies 6.19cm^{2}}$

$\boxed {\underline {\mathbb {GIVEN:-}}}$

• a circle of radius 7cm

• corresponding arc length is 6.2cm

$\boxed {\underline {\mathbb {TO\:FIND:-}}}$

area of the sector of a circle

$\boxed {\underline {\mathbb {FORMULA\:USED:-}}}$

• $length\:of\:arc=\frac{ \theta }{360} \pi r$

• Area of sector $= \frac{\theta}{360} \pi r^{2}$

$\boxed {\underline {\mathbb {SOLUTION:-}}}$

Arc length (length of sector\arc) is 6.2 cm

Radius of circle is 7 cm

$\frac{ \theta }{360} \pi r = 6.2$

$\frac{ \theta }{360} \times \frac{22}{7} \times 7 = 6.2$

$\frac {\theta \times 22 \times 7}{360}=6.2$

$\frac {154 \theta }{360}=6.2$

$\theta = \frac{6.2 \times 360} {154}$

$\theta = 14.49$

Now as we got $\theta$ so let’s put in sector formula to get area of sector

Area of sector $= \frac{\theta}{360} \pi r^{2}$

$= \frac{14.49}{360} \times \frac{22}{7} \times 7^{2}$

$= \frac{ 15620.22 }{2520}$

$= 6.19 cm^{2}$