Question

suppose the radius r is 1.5 units and the angle \\(\theta\\) is \\(\frac{\pi}{3}\\) radians. what is the sector area a? please round to two places after the decimal point.

Explanation:

Step1: Recall the sector area formula

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

Step2: Substitute the given values

We are given \( r = 1.5 \) and \( \theta=\frac{\pi}{2} \). Substitute these values into the formula:
\( A=\frac{1}{2}\times(1.5)^{2}\times\frac{\pi}{2} \)

First, calculate \( (1.5)^{2}=2.25 \). Then the expression becomes:
\( A=\frac{1}{2}\times2.25\times\frac{\pi}{2}=\frac{2.25\pi}{4} \)

Step3: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have:
\( A=\frac{2.25\times3.14159}{4}=\frac{7.0685775}{4} = 1.767144375\)

Step4: Round to two decimal places

Rounding \( 1.767144375 \) to two decimal places gives \( 1.77 \).

Answer:

\( 1.77 \)