Question

Area of a sector of a radius 6 inches and 30 degrees

Answer 1

The area of a sector with a radius of 6 inches and a central angle of 30 degrees is 3π square inches, which is found by taking the fraction of the circle the sector occupies (1/12) and multiplying it by the area of the whole circle.

Step-by-step explanation:

To find the area of a sector with a radius of 6 inches and a central angle of 30 degrees, we can use the formula for the area of a sector, which is (θ/360) × πr², where θ is the central angle in degrees and r is the radius of the circle.

Firstly, calculate the proportion of the circle that the sector represents by dividing the angle by the total number of degrees in a circle, 360 degrees. In this case, 30°/360° = 1/12. This fraction represents the portion of the full circle's area that the sector takes up.

Then calculate the area of the whole circle using the formula πr². With a radius of 6 inches, this would be π × (6 inches)² = 36π square inches.

Multiply the proportion of the circle by the total area to get the area of the sector: (1/12) × 36π = 3π square inches.

Therefore, the area of the sector isb

Answer 2

The area of a sector of a circle with radius
`r` and central angle
`\theta` is


`A=\frac{r^2}2\theta`

which comes from the proportion relation,


`\frac{\text{area of circle}}{\text{one full revolution}}=(\pi r^2)/(2\pi)=\frac A\theta=\frac{\text{area of sector}}{\text{measure of central angle (radians)}}`

You have
`30^\circ=\frac\pi6\text{ rad}`, so the area is


`A=\frac{6^2}2*\frac\pi6=3\pi`