Question

1. find the arc length in the diagram below. round your answer to the nearest tenth. question 5

Explanation:

Step1: Recall arc - length formula

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

Step2: Identify values of $r$ and $\theta$

From the diagram, the radius $r = 16$ cm and the central angle $\theta=\frac{3\pi}{2}$ radians.

Step3: Calculate the arc - length

Substitute $r = 16$ and $\theta=\frac{3\pi}{2}$ into the formula $s=r\theta$. So, $s = 16\times\frac{3\pi}{2}$.
\[

$$\begin{align*} s&=16\times\frac{3\pi}{2}\\ &=8\times3\pi\\ & = 24\pi \end{align*}$$

\]

Step4: Round to the nearest tenth

$24\pi\approx24\times 3.14159 = 75.4$ cm.

Answer:

$75.4$ cm