Answer
Fencing a garden means finding the perimeter of the garden, whereas, to apply fertilizer to the garden, we need to find the area of the garden.
Work Step by Step
The fencing in a garden is done on the boundaries of the garden. The fertilizer is applied inside the garden.
So, for fertilizers, the area of the garden needs to be found.
To do the fencing of a circular garden, the perimeter (or circumference) can be computed as follows:
\[C=2\pi r\]
For the application of fertilizer, the area of the garden would be:
\[A=\pi {{r}^{2}}\]
Example:
If the radius of a circular garden is\[40\text{ft}\text{.}\], the length of fence required would be:
\[\begin{align}
& C=2\pi r \\
& =2\pi \times 40\text{ ft}\text{.} \\
& =80\pi \text{ ft}\text{.}
\end{align}\]
Compute the amount of fertilizer required depending on the area of the garden as follows:
\[\begin{align}
& A=\pi {{r}^{2}} \\
& =\pi {{\left( 40\text{ ft} \right)}^{2}} \\
& =1600\pi \text{ ft}{{.}^{2}}\text{ }
\end{align}\]
