Question

3. Given a circle with a radius of 4 inches and a central angle of 170°, find the arclength and the sector area.

Answer 1

Use the following formula for the sector area:

$A=\frac{\theta}{360}\cdot\pi r^2$

where,

θ = 170

π = 3.14

r: radius = 4 in

Replace the previous values of the parameters into the formula for A and simplify:

$A=\frac{170}{360}(3.15)(4in)^2=23.8in^2$

Hence, the sector area is 23.8 in^2

To find the measure of the arclength, use the following formula:

$s=2\pi r\cdot\frac{\theta}{360}=2(3.14)(4in)\cdot\frac{170}{360}\approx11.86in$

Hence, the arclength is approximately 11.86 in