Question

If the area of a sector of a circle is 5/8 of the area of the circle, then the sector angle is
equal to

(a) 60°
(b) 90°
(C) 100°
(d) 225°

Answer 1

[d] 225°

$\mathcal\green{\underbrace{\red{SOLUTION:-}}}$

GIVEN :-

✍️ The area of a sector of a circle is 5/8 of the area of the circle .

$\checkmark\:\rm{\blue{Area\:of\:the\:sector\:=\:\dfrac{5}{8}\:\times{Area\:of\:the\:circle\:}\:}}$

FORMULA :-

$\bigstar\:\mathcal{\red{\boxed{\purple{Area\:of\:Sector\:=\:\dfrac{\theta}{360}\:\times{\pi\:r^2}\:}}}}$

$\bigstar\:\mathcal{\red{\boxed{\purple{Area\:of\:Circle\:=\:\pi\:r^2\:}}}}$

CALCULATION :-

$\rm{\implies\:\dfrac{\pi}{360}\:\times{\pi\:r^2}\:=\:\dfrac{5}{8}\:\times{\pi\:r^2}\:}$

$\rm{\implies\:\pi\:=\:\dfrac{5}{8}\:\times{360}\:}$

$\rm{\implies\:\pi\:=\:5\times{45}\:}$

$\rm{\red{\boxed{\implies\:\pi\:=\:225^{\degree}\:}}}$

$\therefore\:\rm{\green{The\:angle\:of\:the\:sector\:is\:\:225^{\degree}\:.}}$

Answer 2

Step-by-step explanation:

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