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 let's people reduce the radius by up to 25percent. 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?

Accepted Solution

Answer:Area_lawn = 393.75 π ft^2Step-by-step explanation:Maximum radius : 30 feetMinimum radius:  30 feet - 0.25*(30feet)  =  22.5 feet(25 percent reduction)To find the area of lawn that can be watered, we just need to calculate the area for the maximum radius and the minimum radius, and then subtract them.Since the sprinklers have a circular area:Area = π*radius^2Max area  = π*(30 ft)^2 = 900π ft^2Min area  = π*(22.5 ft)^2 = 506.25π ft^2Maximum area of lawn that can be watered by the sprinkler:Area_lawn = Max area - Min area = 900π ft^2 -506.25π ft^2Area_lawn = 393.75 π ft^2