Question

a circle has a radius of 4 ft. what is the area of the sector formed by a central angle measuring \\( \frac { 3 \pi } { 2 } \\) radians? use 3.14 for pi. enter your answer as a decimal in the box

Explanation:

Step1: Recall the formula for the area of a sector

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

Step2: Substitute the given values into the formula

Given \(r = 4\) ft and \(\theta=\frac{3\pi}{2}\). Substitute into \(A=\frac{1}{2}r^{2}\theta\):

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Step3: Substitute \(\pi = 3.14\)

Substitute \(\pi = 3.14\) into \(A = 12\pi\):
\(A=12\times3.14 = 37.68\)

Answer:

\(37.68\)