a sprinkler that sprays water in a circular area can be adjusted to spray up to 30 feet. To the nearest tenth, what is the maximum area of lawn that can be watered by the sprinkler?
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Answer:
Answer: 1590.4 square feet
Step-by-step explanation:
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College Mathematics 5 points
Paris020605
Paris020605
Asked 04.01.2019
A sprinkler that sprays water in a circular area can be adjusted to spray up to 30 feet. turning the radius-reduction screw on the top of the nozzle lets people the radius by up to 25 percent. to the nearest tenth, what is the maximum area of lawn that can be watered by the sprinkler if the radius-reduction is used at full capacity.
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Answer: 1590.4 square feet
Step-by-step explanation:
Given: The radius of the circular area = 30 feet
Now, 25% of the radius = 0.25\times30=7.5 feet
If the we reduce the radius by 25%, then the radius of the circular area =
30-7.5=22.5\text{ feet}
Now, the circular area of the spray is given by :-
\text{Area}=\pi r^2\\\\\Rightarrow\text{ Area}=(3.143.141592653)(22.5)^2\\\\\Rightarrow\text{ Area}=1590.43128088\approx1590.4\text{ ft}^2
Therefore, the maximum area of lawn that can be watered by the sprinkler if the radius-reduction is used at full capacity = 1590.4 square feet.
The maximum area of lawn that can be watered by the sprinkler is 2826 sq feet
Solution:
Given that,
A sprinkler that sprays water in a circular area can be adjusted to spray up to 30 feet
Therefore,
radius = 30 feet
The area of circle is given as:
Thus, maximum area of lawn that can be watered by the sprinkler is 2826 sq feet
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