A circle has a radius of 8cm. A sector of the circle has a central angle of (2pi )/(3) radians. Find the area of the sector. Do not round any Intermediate computations Round your answer to the nearest tenth.

## Step 1<br />The problem involves finding the area of a sector of a circle. The formula for the area of a sector is given by:<br />### \(A = \frac{\theta}{2\pi} \times \pi r^2\)<br />where \(A\) is the area of the sector, \(\theta\) is the central angle in radians, and \(r\) is the radius of the circle.<br /><br />## Step 2<br />In this problem, the radius \(r\) is given as 8 cm and the central angle \(\theta\) is given as \(\frac{2\pi}{3}\) radians.<br /><br />## Step 3<br />Substitute the given values into the formula:<br />### \(A = \frac{\frac{2\pi}{3}}{2\pi} \times \pi \times (8)^2\)<br /><br />## Step 4<br />Simplify the expression:<br />### \(A = \frac{1}{3} \times \pi \times 64\)<br /><br />## Step 5<br />Calculate the area:<br />### \(A = \frac{64\pi}{3}\)<br /><br />## Step 6<br />Round the answer to the nearest tenth:<br />### \(A \approx 67.2\)