Question

Determine the area of the sector :

A circle with radius 12 inches formed by a central angle of 165°:

Round your answer to two decimal places.

______ inches squared

Answer 1

Answer:

$\boxed {\boxed {\sf a \approx207.35 \ in^2}}$

Step-by-step explanation:

Since the central angle is given in degrees, we should use this formula to find the area of the sector:

$a=\frac{\theta}{360} \times \pi r^2$

The central angle is 165 degrees and the radius is 12 inches.

• θ= 165
• r= 12 in

Substitute the values into the formula.

$a= \frac{165}{360} \times \pi (12 \ in)^2$

Solve the exponent.

• ( 12 in)² = 12 in * 12 in =144 in²

$a= \frac{165}{360} \times \pi(144 \ in^2)$

Multiply all the numbers together.

$a= 207.345115137 \ in^2$

Round to the nearest hundredth (two decimal places).

• 207.345115137

The 5 in the thousandth place (in bold above) tells us to round the 4 in the hundredth place up to a 5.

$a \approx207.35 \ in^2$

The area of the sector is approximately 207.35 inches squared.