Question

1 fill in the blark
the image shov circle with a shaded sector.
if you leave your answer in terms of π, write out the word pi. if you leave your answer as a decimal, round to the hundredths place.
1 find the area of the shaded sector. square feet

1. find the length of the arc defined by the sector. feet

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector of a circle is \(A=\frac{\theta}{360}\times\pi r^{2}\), where \(\theta\) is the central angle of the sector and \(r\) is the radius of the circle.
Given \(\theta = 60^{\circ}\) and \(r = 30\) ft.
Substitute the values into the formula:
\(A=\frac{60}{360}\times\pi\times(30)^{2}\)
\(=\frac{1}{6}\times\pi\times900\)
\( = 150\pi\)
If we calculate the decimal value: \(A=150\times3.14 = 471.00\) square feet.

Step2: Recall the formula for the arc - length of a sector

The formula for the arc - length \(L\) of a sector of a circle is \(L=\frac{\theta}{360}\times2\pi r\), where \(\theta\) is the central angle of the sector and \(r\) is the radius of the circle.
Given \(\theta = 60^{\circ}\) and \(r = 30\) ft.
Substitute the values into the formula:
\(L=\frac{60}{360}\times2\pi\times30\)
\(=\frac{1}{6}\times60\pi\)
\( = 10\pi\)
If we calculate the decimal value: \(L=10\times3.14=31.40\) feet.

Answer:

1. \(150\pi\) (or \(471.00\)) square feet
2. \(10\pi\) (or \(31.40\)) feet