Question

A sprinkler sprays water in a circular area up to 30 feet. A radius reduction screw lets people reduce the radius by up to 25%. What is the maximum area of lawn that can be watered if the radius reduction is at full capacity.

Answer 1

Answer:
`1590.63\ ft^2`

Explanation:

Given

The sprinkler can water the area up to
`30\ ft` i.e.
`30\ ft` is the radius

If the screw leads to a reduction of 25% in radius, then the new radius is

`r'=(1-0.25)r\\r'=0.75r\\r'=22.5\ ft`

So, the area corresponding to this radius

`\Rightarrow \pi (22.5)^2\\\Rightarrow 1590.63\ ft^2`

Thus, the maximum area that can be covered is
`1590.63\ ft^2`