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(\pi d)/(\pi)=(322)/(\pi) \\ \Rightarrow d=(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=(d)/(2) \\ \Rightarrow r=((322)/(\pi))/(2)=(322)/(2\pi)=(161)/(\pi)\text{ in.}\approx51.2\text{ in.} \end{gathered}`

The radius is 51.2 in.

The diameter is 102.5 in.