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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.

Respuesta :

Answer: [tex]1590.63\ ft^2[/tex]

Step-by-step explanation:

Given

The sprinkler can water the area up to [tex]30\ ft[/tex]  i.e. [tex]30\ ft[/tex]  is the radius

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

[tex]r'=(1-0.25)r\\r'=0.75r\\r'=22.5\ ft[/tex]

So, the area corresponding to this radius

[tex]\Rightarrow \pi (22.5)^2\\\Rightarrow 1590.63\ ft^2[/tex]

Thus, the maximum area that can be covered is [tex]1590.63\ ft^2[/tex]

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