Question

calculator
a circular sector has a central angle of \\( \frac{\pi}{6} \\) radians and a radius of 9 ft.
what is the area of the sector?
use 3.14 for pi. round your answer to the nearest tenth.
enter your answer in the box.
area = \\( \square \\) \\( \mathrm{ft}^{2} \\)

Explanation:

Step1: Recall the formula for the area of a sector

The formula for the area of a sector is \(A=\frac{1}{2}r^{2}\theta\), where \(r\) is the radius and \(\theta\) is the central angle in radians.

Step2: Substitute the given values into the formula

Given \(r = 9\) ft and \(\theta=\frac{\pi}{6}\). Substitute into \(A=\frac{1}{2}r^{2}\theta\), we get \(A=\frac{1}{2}\times9^{2}\times\frac{\pi}{6}\).
First, calculate \(9^{2}=81\). Then the formula becomes \(A=\frac{1}{2}\times81\times\frac{\pi}{6}\).
\(A=\frac{81\pi}{12}\).
Since \(\pi = 3.14\), then \(A=\frac{81\times3.14}{12}\).
\(81\times3.14 = 254.34\). So \(A=\frac{254.34}{12}\).

Step3: Calculate the value

\(\frac{254.34}{12}=21.195\).

Step4: Round to the nearest tenth

Rounding \(21.195\) to the nearest tenth. The digit in the hundredth place is \(9\), so we round up the digit in the tenth place. \(21.195\approx21.2\).

Answer:

\(21.2\)