Question

A circle has an area of 153.86 units2 and a circumference of 43.96 units. If the radius is 7 units, what can be said about the relationship between the area and the circumference? (Use 3.14 for .)

Answer 1

Explanation:

`\text{Circumference:}\\\\C=2\pi r\\\\\text{Area:}\\\\A=\pi r^2\\\\(A)/(C)=(\pi r^2)/(2\pi r)\qquad\text{cancel}\ \pi\ \text{and}\ r\\\\(A)/(C)=(r)/(2)\\\\\bold{The\ number\ of\ areas\ of\ a\ circle\ is}\ (r)/(2)\ \bold{larger\ than\ its\ circumference}.`

`\text{For a given area and circumference}:\\\\A=153.86,\ C=43.96,\ r=7\\\\(A)/(C)=(153.86)/(43.96)=3.5=(7)/(2)=(r)/(2)\\\\(A)/(C)=(r)/(2)`