Question

Find the missing quantities for the following circle. Use the pi key for pi.Use a calculator value for π.(Type an integer or decimal rounded to the nearest tenth as needed.)

Answer 1

It is given that the circle has a circumference of 322 in.

It is required to find its radius and diameter.

Recall that the circumference of a circle with diameter d is given as:

$C=\pi d$

Substitute C=322 into the formula:

$\begin{gathered} 322=\pi d \\ \text{ Swap the sides:} \\ \Rightarrow\pi d=322 \\ \text{ Divide both sides by }\pi: \\ \Rightarrow\frac{\pi d}{\pi}=\frac{322}{\pi} \\ \Rightarrow d=\frac{322}{\pi}\text{ in.}\approx102.5\text{ in.} \end{gathered}$

Recall that the radius is one-half of the diameter. It follows that:

$\begin{gathered} r=\frac{d}{2} \\ \Rightarrow r=\frac{\frac{322}{\pi}}{2}=\frac{322}{2\pi}=\frac{161}{\pi}\text{ in.}\approx51.2\text{ in.} \end{gathered}$

The radius is 51.2 in.

The diameter is 102.5 in.