Question

A circle has an area of 1375 sq cm If a sector of the circle has an area of 275 sq cm, find its angular measure.​

Answer 1

Answer:

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Answer 2

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

• Area of circle = 1375 cm²
• Area of Sector = 275 cm²

Solution

We have formula for area of circle :

$\Large{\boxed{\boxed{\sf{Area \: = \: \pi r^2}}}}$

$\rightarrow 1375 = \: \pi {r}^{2} \\ \rightarrow {r}^{2} \: = \: \dfrac{1375}{ \pi} \\ \\ \implies \large{ \boxed{ \sf{ {r}^{2} \: = \: \frac{1375}{ \pi} }}}$

Now use formula for area of sector :

$\Large{\boxed{\boxed{\sf{Area \: = \: \dfrac{\pi r^2 (\theta) }{360^{\circ}}}}}}$

Put Values

Put value of r²

$\rightarrow 275 \: = \: \dfrac{\cancel{\pi} \: \frac{1375}{\cancel{\pi}} (\theta) }{360}$

$\rightarrow 275 \: = \: \dfrac{1375 \theta}{360}$

$\rightarrow 275 \: \times \: 360 \: = \: 1375 \theta$

$\rightarrow 9900 \: = \: 1375 \theta$

$\rightarrow \theta \: = \: \dfrac{9900}{1375}$

$\rightarrow \theta \: = \: 72^{\circ}$

$\LARGE {\underline{\boxed{\sf{\theta \: = \: 72^{\circ}}}}}$