Required information
A wheel of radius $30.0 \mathrm{~cm}$ is rotating at a rate of 3.30 revolutions every $0.0710 \mathrm{~s}$.
Through what angle does the wheel rotate in $1.00 \mathrm{~s}$ ?
$\mathrm{rad}$

Step 1 ：Given that the wheel is rotating at a rate of 3.30 revolutions every 0.0710 seconds, we first need to convert this rate into revolutions per second. This can be done by dividing the number of revolutions by the time in seconds.

Step 2 ：\(\text{revolutions per second} = \frac{3.30}{0.0710} = 46.47887323943662\)

Step 3 ：Next, we convert the rate of rotation from revolutions per second to radians per second. This can be done by multiplying the rate of rotation by \(2\pi\), since one revolution is equal to \(2\pi\) radians.

Step 4 ：\(\text{radians per second} = 46.47887323943662 \times 2\pi = 292.03537343229067\)

Step 5 ：Finally, to find the angle through which the wheel rotates in 1 second, we simply multiply the rate of rotation in radians per second by the time of 1 second.

Step 6 ：\(\text{angle} = 292.03537343229067 \times 1.0 = 292.03537343229067\)

Step 7 ：Final Answer: The wheel rotates through an angle of \(\boxed{292.04 \, \text{rad}}\) in 1 second.