Question

Suppose that you needed to make a pen for some small animals. You have 12.0 m of fencing. You decide to make a circular pen, because if you wish to enclose an area using a given length of fencing, then a circular fence encloses a larger area than a fence of any other shape. What is the area A of the pen

Answer 1

`A = 11.465\ m^2`

Explanation:

Given

`Fencing = 12\ m`

Required

Determine the area of the pen

The given parameter represents the perimeter of the pen;

Since, the pen is circular, we have circumference, C:

`C = 2\pi r`

Substitute 12 for C

`12 = 2\pi r`

Divide through by 2

`6 = \pi r`

Make r the subject of formula

`r = (6)/(\pi)`

The area (A) of the pen is calculated as follows;

`A = \pi * r^2`

Substitute
`(6)/(\pi)` for r

`A = \pi * ((6)/(\pi))^2`

Open Bracket

`A = \pi * (36)/(\pi^2)`

`A = (36)/(\pi)`

Take
`\pi` as 3.14

`A = (36)/(3.14)`

`A = 11.465\ m^2` (Approximated)