# How many minutes would it take to completely empty the tub at that rate? A full cylindrical hot tub with a height of 4 feet and a radius of 3 feet is being emptied at a rate of 5 ft^3 every 2 minutes. How many minutes would it take to completely empty the tub at that rate?

The cylindrical hot tub is being emptied at a rate 5 ft^3 / 2 minutes or (5/2) ft^3 per minute.

The height of the tub is 4 feet and the radius of the tub is 3 feet.

For a cylinder with a height h and a radius r, the volume...

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The cylindrical hot tub is being emptied at a rate 5 ft^3 / 2 minutes or (5/2) ft^3 per minute.

The height of the tub is 4 feet and the radius of the tub is 3 feet.

For a cylinder with a height h and a radius r, the volume is given by pi*r^2*h. Substituting the values r = 3 and h = 4, we get

V = pi*3^2*4

=> V = pi*9*4

=> 36*pi ft^3

The rate at which the tub is being emptied is (5/2) ft^3/minute.

This gives the time required to empty the tub as 36*pi / (5/2)

=> pi*36*2/5

=> pi*14.4 minutes

The required time to completely empty the tub is 14.4*pi minutes.

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