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Answer:
Option D. 5890.5 feet²
Step-by-step explanation:
An individual head of a sprinkler system covers a circular are of grass with a radius of 25 feet.
Yard has three sprinkler heads that each cover circular area with no overlap.
We have to calculate the approximate area watered by these 3 sprinkler heads.
Area covered by one sprinkler = π×r² = π×(25)² = 625π feet²
Therefore area covered by three sprinkler heads = 3 × 625π = 5892.85 feet²
which matches the approximate value of Option D. 5890.5 feet²
A circle is a curve sketched out by a point moving in a plane. The approximate total area that will be watered is 5890.5 ft³.
What is a circle?
A circle is a curve sketched out by a point moving in a plane so that its distance from a given point is constant; alternatively, it is the shape formed by all points in a plane that are at a set distance from a given point, the centre.
The radius of the circular area in which a sprinkler can water is 25 feet. Therefore, the area of the circular area will be equal to,
[tex]\rm \text{Area of the Sprinkler}= \pi r^2= \pi \times 25^2 = 1,963.4954\ ft^2[/tex]
The area that will be covered by three sprinklers will be equal to,
[tex]\rm \text{Area covered byt three sprinkler} = 3 \times \text{Area covered by a single sprinkler}\\\\\text{Area covered byt three sprinkler} = 3 \times 1,963.4954\ ft^3 = 5,890.4862\ ft^3[/tex]
Hence, the approximate total area that will be watered is 5890.5 ft³.
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