Landscaper A landscaper has installed a circular sprinkler...

Landscaper $A$ landscaper has installed a circular sprinkler system that covers an area of 1800 square feet. (a) Find the radius of the region covered by the sprinkler system. Round your answer to three decimal places. (b) If the landscaper wants to cover an area of 2400 square feet, how much longer does the radius need to be?

Landscaper $A$ landscaper has installed a circular sprinkler system that covers an area of 1800 square feet.
(a) Find the radius of the region covered by the sprinkler system. Round your answer to three decimal places.
(b) If the landscaper wants to cover an area of 2400 square feet, how much longer does the radius need to be?

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Key Concepts

Area of a Circle

This concept deals with the formula used to calculate the area of a circle, which is A = ?r², where A is the area and r is the radius. It is fundamental in geometry and is applied in a variety of contexts where circular regions or objects are analyzed.

Solving for the Radius

When the area of a circle is given, the radius can be found by rearranging the area formula to r = ?(A/?). This involves algebraic manipulation and understanding of square roots, and is a key technique in problems involving circles.

Rounding and Precision

In many real-world and mathematical problems, numerical results need to be rounded to a specified number of decimal places. This requires understanding of significant figures and rounding rules to ensure that the answer is both precise and accurate.

Comparing Changes in Geometric Dimensions

This concept involves understanding how changes in one geometric dimension, such as the radius, affect other properties, like area. When comparing two areas, determining the difference in the corresponding radii requires using the relationship between area and radius and understanding the implications of scaling in circular shapes.

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