Question

Length of minor arc of a circle of radius 10 cm is 14cm. Find the area of minor sector of a circle. Pls help its urgent!

Answer 1

We have,

• Central angle = θ
• Radius of the circle (r) = 10 cm
• Length of minor arc = 14 cm
• Value of π = 3.14

$\boxed{\bold{Length\: of\: minor\: arc\:=2\pi r \times \frac{\theta}{360}}}$

Applying the values to the equation,

$\implies\bold{14=2\times3.14\times10\times\frac{\theta}{360}}$

$\implies\bold{\theta=\frac{360\times14}{3.14\times2\times10}}$

$\implies\bold{\theta=\frac{5040}{62.8}}$

$\boxed{\bold{\theta=80.254}}$

$\boxed{\bold{Area\: of\: minor\: Sector\:=\pi r^2 \times \frac{\theta}{360}}}$

Applying the values to the equation,

$\implies\bold{Area=3.14\times 10^2\times\frac{80.254}{360}}$

$\boxed{\bold{\therefore{Area=70\:cm^2}}}$