A cylindrical tank with a radius of 6 feet is being filled with water at a rate of 4 cubic feet per minute. How long will it take to fill the tank to a depth of 9 feet?
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To find the time it will take to fill the tank to a depth of 9 feet, we first need to calculate the volume of water needed to fill the tank to that depth.
The volume of a cylinder can be calculated using the formula V = πr^2h, where V is the volume, r is the radius, and h is the height.
In this case, the radius is 6 feet and the height is 9 feet. Plugging these values into the formula, we get:
V = π(6^2)(9)
V = π(36)(9)
V = 324π
So, the volume of water needed to fill the tank to a depth of 9 feet is 324π cubic feet.
Since the water is being filled at a rate of 4 cubic feet per minute, it will take:
Time = volume / rate
Time = 324π / 4
Using a calculator or approximating π as 3.14, we can calculate:
Time = 324(3.14) / 4
Time = 810.36 / 4
Time ≈ 202.59 minutes
Therefore, it will take approximately 202.59 minutes to fill the tank to a depth of 9 feet.
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