Question

An individual head of a sprinkler system covers a circular area of grass with a radius of 25 feet. The yard has 3 sprinkler heads that each cover a circular area with no overlap. What is the approximate total area that will be watered? 1963. 5 ft 1963. 5 ft² 5890. 5 ft 5890. 5 ft².

Answer 1

The total area covered by the yard by the 3 sprinkler heads such that each covers a circular area with no overlap is 5892.857 ft².

What is the area of a circle?

The area of a circle is the area covered by the circle with radius r. It is given by the formula,

$\text{Area of circle} = \pi r^2$

As it is given that the area covered by a single sprinkler system is of the radius of 25 feet, therefore, the area covered by a singular sprinkler system can be written as,

Area of sprinkler = Area of a circle with radius 25 feet

 $\begin{aligned}\text{Area of sprinkler}&= \pi r^2\\&=\pi (25^2)\\&= 1964.2857 \approx 1964.286\rm\ ft^2\end{aligned}$

Now, as we know that the yard has three such sprinkler systems, therefore, the area covered by the sprinkler will be thrice the area covered by a single sprinkler,

The total area covered by the sprinkler = 3 x Area of sprinkler

                                                                   = 3 x 1964.286

                                                                   = 5892.857

Thus, the total area covered by the yard by the 3 sprinkler heads such that each covers a circular area with no overlap is 5892.857 ft².

Learn more about the Area of Circle:

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