The amount Q of water emptied by a pipe varies directly as the square of the diameter d. A pipe 5 inches in diameter will empty 50 gal of water over a fixed time period. Assuming the same kind of flow, how many gallons of water are emptied in the same amount of time by a pipe that is 2 inches in diameter?
gallons are emptied.

Q= 8

The amount emptied is 8 gallons of water

Step-by-step explanation:

First we need to create the equation for the above statement.

Q is directly proportional to the square of d

Q= kd²

Q= 50

d= 5

50= k5²

50 = k25

K = 50/25

K = 2

K is the constant of proportionality.

Now our equation is

Q= 2d²

Where Q = volume in gallons

d = pipe diameters in inch

For a pipe of diameter 2 inch

The amount of gallons of water emptied assuming the same kinf of flow is

Q= 2d²

Q= 2(2)²

Q= 2(4)

Q= 8

The amount emptied is 8 gallons of water

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