SOLUTION: The power produced by a windmill varies directly with the square of its diameter and the cube of the wind speed. A fan with a diameter of 2.5 meters produces 560 watts of power if

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Question 980442: The power produced by a windmill varies directly with the square of its diameter and the cube of the wind speed. A fan with a diameter of 2.5 meters produces 560 watts of power if the wind speed is 4 m/s. How much power would a similar fan produce if it had a diameter of 6 meters and the wind speed was 5 m/s?
Answer by ikleyn(52835) About Me  (Show Source):
You can put this solution on YOUR website!

The condition of this problem means  exactly the following:

The power produced by a windmill  is proportional to the product of the square of its diameter and the cube of the wind speed.

In other words,

P = k.D%5E2.w%5E3,

where  P  is the power produced by a windmill,  D  is a windmill diameter,  w  is the wind speed,  and  k is the proportionality coefficient which is the constant value for the selected unit system.

Therefore,  the proportion is valid
P%5B2%5D%2FP%5B1%5D = %28D%5B2%5D%2FD%5B1%5D%29%5E2.%28w%5B2%5D%2Fw%5B1%5D%29%5E3 = %284%2F2.5%29%5E2.%285%2F4%29%5E3 = 1.6%5E2.1.25%5E3 = 2.56*1.953 = 5.

where the index  "1"  relates to the  "smaller windmill",  and the index  "2"  relates to the  "larger windmill".

Finally,  its gives P%5B2%5D = 5.P%5B1%5D = 5*560 watts = 2800 watts.