Question

A circle has a radius of 6 inches. Find the area of a sector of this circle that is intercepted by a central angle measuring 30°. A. 2π. B. 3π. C. 6π. D. 12π

Answer 1

The area of the sector of a circle is expressed in the formula: A = 1/2 r^2 * theta where theta is expressed in radians. In this case, we are given with r equal to 6 inches and theta equal to pi/3. Hence the area of the sector is equal to 18.85 cm2 or 6 pi cm2.

Answer 2

Answer:

Option B is correct

3π

Step-by-step explanation:

Area(A) of sector  of the circle is given by:

$A = \pi r^2 \cdot \frac{\theta}{360^{\circ}}$      ....[1]

As per the statement:

A circle has a radius of 6 inches.

⇒r = 6 inches

It is also given that a central angle is 30°

⇒$\theta = 30^{\circ}$

Substitute the given values in [1] we have;

$A = \pi \cdot 6^2 \cdot \frac{30^{\circ}}{360^{\circ}}$

⇒$A = \pi \cdot 36 \cdot \frac{1}{12}$

⇒$A = \pi \cdot 3$

Simplify:

$A = 3 \pi$ square inches

Therefore, the area of a sector of circle is, 3π inches