Chapter 11.8, Problem 36HP

To determine

To compute the area of the circle.

Answer to Problem 36HP

Area $a=\pi \times r^2$

  $=\frac{\pi \times d^2}{4}$

  $a=\frac{c^2}{4\times \pi }$

Explanation of Solution

Given information: Circumference, radius and diameter.

The area and circumference have the same numerical values. On equating the two, the radius ‘r’ can be found out.

Circumference $c=2\times \pi \times r$

Area $a=\pi \times r^2$

Diameter $d=2r$ or $r=\frac{d}{2}$

To find the area, each of these equations shall be used in the formula $a=\pi \times r^2$ , with replacing the value of ‘r’ for various variables.

From radius, area $a=\pi \times r^2$

From circumference, $c=2\times \pi \times r$

or, $r=\frac{c}{2\times \pi }$

  $a=\pi \times \frac{c}{2\times \pi }\times \frac{c}{2\times \pi }$ Dividing value of ‘pi’ from numerator and denominator.

  $a=\frac{c^2}{4\times \pi }$

From diameter

  $a=\frac{\pi \times d^2}{4}$