Question

8. Determine the area of a sector

with a central angle of 42° in a
circle with radius 3 inches.

NEED IT ASAP

Answer 1

`\boxed {\boxed {\sf A \approx 3.3 \ in^2}}`

Explanation:

Since we are given the central angle in degrees, we should use the following formula for sector area.

`A= \frac {\theta}{360}* \pi r^2`

The angle is 42 degrees and the radius is 3 inches. Therefore,

`\theta= 42 \\r=3 \ in`

`A=\frac {42}{360} * \pi (3 \ in)^2`

Solve the exponent.

• (3 in)²= 3 in*3in = 9 in²

`A=\frac {42}{360} * \pi (9 \ in^2)`

Multiply all three numbers together.

`A= 0.116666666667* 3.14159265359 * 9 \ in^2`

`A=3.29867228627 \ in^2`

Let's round to the tenth place. The 9 in the hundredth place tells us to round the 2 up to a 3.

`A \approx 3.3 \ in^2`

The area of the sector is approximately 3.3 square inches.