Chapter 12.2, Problem 30HP

To determine

To find : Difference between circumference and area of a circle and explain formulas relation between them.

Answer to Problem 30HP

Circumference is length of circular region and area is enclosed inside region

  $A=\frac{c^2}{4\pi }$ . Relation between area and circumference.

Explanation of Solution

Given information :

The given information is, Circumference and area of circle.

Formula Used:

Circumference, $c=2\pi r$ , Area, $A=\pi r^2$

Calculation :

Circumference is distance around the circular region, total length of boundary line of region, whereas area is measure of enclosed region, inside circle, inside boundary wall.

Measurement of circumference is in in/ft/cm whereas Area is in m²/ft²/cm² relation between area and circumference.

  $\begin{array}{l}A=\pi {\left(\frac{c}{2\pi }\right)}^2,\left[\because c=2\pi r,\Rightarrow r=\frac{c}{2\pi }\right]\\ \Rightarrow A=\frac{\pi c^2}{4{\pi }^2}\end{array}$

  $\Rightarrow A=\frac{c^2}{4\pi }$ , where $c$ is circumference.