Question

♡ Maths Question ♡

Find the area of sector of a circle with radius 6 cm If angle of sector is 30°.

Answer 1

Given:-        

• Radius of a circle is 6 cm.
• Angle of the sector is 30°.

To find:-        

• The area of sector of a circle  

Solution:-        

Here, we have given that the radius of the circle is 6 cm and the angle of the sector is 30°.

So to find out the area of sector of a circle, we will use the formula.

• Area of the sector - Θ/360° ×πr²  

Where,

• Θ = 30°
• π = 22/7
• r = 6 cm

♡ On applying formula  ♡

$\qquad\tt{:\implies\:Area\:of\:sector\:=\:\dfrac{\theta}{360^{\circ}}\:\times\:\pi\:r^{2}}$

$\qquad\tt{:\implies\:Area\:of\:sector\:=\:\dfrac{30^{\circ}}{360^{\circ}}\:\times\:\dfrac{22}{7}\:\times\:6\:\times\:6}$

$\qquad\tt{:\implies\:Area\:of\:sector\:=\:\dfrac{3}{36}\:\times\:\dfrac{22}{7}\:\times\:6\:\times\:6}$

$\qquad\tt{:\implies\:Area\:of\:sector\:=\:\dfrac{1}{12}\:\times\:\dfrac{22}{7}\:\times\:6\:\times\:6}$

$\qquad\tt{:\implies\:Area\:of\:sector\:=\:\dfrac{1}{2}\:\times\:\dfrac{22}{7}\:\times\:6\:}$

$\qquad\tt{:\implies\:Area\:of\:sector\:=\:\dfrac{22}{7}\:\times\:3\:}$

$\qquad\tt{:\implies\:Area\:of\:sector\:=\:\dfrac{22}{7}\:\times\:\dfrac{3}{1}\:}$

$\qquad\tt{:\implies\:Area\:of\:sector\:=\:\dfrac{66}{7}}$

$\therefore\underline{\bf{The\:Area\:of\:the\:sector\:is\:\dfrac{66}{7}\:cm^{2}\:.}}$

Answer 2

Answer:

Given:

Radius =r=6 cm and θ=30

∘

Area of sector

=

360

θ

(πr

2

)

=

360

30

×3.14×(6)

2

=9.42 cm

2