Question

A water sprinkler sprays water to a distance of \[216cm\] in all directions. Find the area with sprinkler water.

Answer 1

Hint: The water sprinkler sprays water to a distance of \[216cm\] in all directions means it can spray up to a circle whose radius is \[216cm\].
The area with its sprinkler water is the area of the circle whose radius is \[216cm\]. Therefore we are going to find the area of the circle of radius \[216cm\].

Complete step-by-step answer:
     

It is given that the water sprinkler sprays water to a distance of 216 cm in all directions.
If the water sprinkler is at the point O, it can spray water to a distance of 216 cm in all direction
That is the water sprinkler sprays water in a circular path.
Therefore it can spray along or in the circle of radius r=216cm.
We have to find out the area where it sprinkles water.
That is nothing but the area of the circular path with radius 216cm.
So, the area which its sprinkler water is found using the formula \[\pi {r^2}\]
Let us substitute the value of r we get,
\[ = \dfrac{{22}}{7} \times 216 \times 216\]
\[ = \dfrac{{1026432}}{7}\]
The area which the water sprinkles is \[146633.14c{m^2}\]
Hence, the area which its sprinkler water is \[146633.14c{m^2}\]

Note: A circle is a shape consisting of all the points in a plane that are a given distance from a given point, the centre, equivalently it is the curve traced out by a point that moves in a plane so that its distance from a given point is constant.
If the radius is r cm then the area of the circle is \[\pi {r^2}c{m^2}\] .