how long is the arc intersected by a central angle of $\frac{pi}{2}$ radians in a circle with a radius of…

Explanation:

Step1: Recall arc - length formula

The formula for the length of an arc $s$ of a circle is $s = r\theta$, where $r$ is the radius of the circle and $\theta$ is the central angle in radians.

Step2: Substitute given values

We are given that $r = 4.5$ cm and $\theta=\frac{\pi}{2}$ radians. Substituting these values into the formula, we get $s=4.5\times\frac{\pi}{2}$.

Step3: Approximate $\pi$ and calculate

Using $\pi = 3.14$, we have $s = 4.5\times\frac{3.14}{2}=\frac{4.5\times3.14}{2}=\frac{14.13}{2}=7.065$ cm.

Step4: Round to the nearest tenth

Rounding $7.065$ to the nearest tenth gives $7.1$ cm.

Answer:

D. $7.1$ cm