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 is 3π square inches.

Step-by-step explanation:

To find the area of a sector of a circle, you need to use the formula:

Area of sector = (central angle/360) × πr²

In this case, the central angle is 30° and the radius is 6 inches. Plugging in these values, we get:

Area = (30/360) × π × 6² = (1/12) × π × 36 = 3π square inches

Therefore, the area of the sector is 3π, which corresponds to option B.

Answer 2

Option B is correct

3π

Step-by-step explanation:

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

`A = \pi r^2 \cdot (\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 (30^(\circ))/(360^(\circ))`

⇒
`A = \pi \cdot 36 \cdot (1)/(12)`

⇒
`A = \pi \cdot 3`

Simplify:

`A = 3 \pi` square inches

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