Question

A circle has a radius of 6 cm. What is the area of a sector subtended by an angle of 30 degrees

Answer 1

Answer:

$3\pi$

Step-by-step explanation:

Since the total angle measure of a circle is 360 degrees, a 30 degree sector is 30/360=1/12 of the area of the circle. Since the area of the full circle is $\pi r^2=\pi \cdot 6^2=36\pi$, the area of the sector is $3\pi$ square centimeters. Hope this helps!

Answer 2

Area of the sector subtended by an angle of 30degrees is equals to $3\pi$.

What is area of the sector?

" Area of the sector is defined as the total amount of space occupied by the two radii and the arc enclosed in it."

Formula used

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

r = radius of the circle

θ = central angle

According to the question,

Given ,

Radius of the circle ' r'= 6cm

Central angle 'θ' = 30 degrees

Substitute the value in the area of the sector formula we get,

Area of the sector = $\pi (6)^{2} (\frac{30}{360})$

                              = $\pi (36)(\frac{1}{12})$

                              = $3\pi$

Hence, area of the sector is equals to $3\pi$.

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