A cylinder is leaking water but you are unable to determine at what rate. The cylinder has a height of 2 m and a radius of 2 m. Find the rate at which the water is leaking out of the cylinder if the rate at which the height is decreasing is 10 cm/min when the height is 1 m.

The rate at which the water is leaking out of the cylinder if the rate at which the height is decreasing is 10 cm/min when the height is 1 m is -1.256cm³/min

The formula for calculating the volume of the cylinder is expressed as:

Taking the derivative of the function with respect to the height

Given the following parameters

Since the radius is constant, hence:

Hence the rate at which the water is leaking out of the cylinder if the rate at which the height is decreasing is 10 cm/min when the height is 1 m is -1.256cm³/min

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Step-by-step explanation:

Volume of a Cylinder,V=

Height = 2m

Radius=2m

When h=1m,

The radius of the cylinder does not change, so we treat it as a constant.

The water is leaking out at a rate of

4444444444444 i think

look at the picture.

y-intercept for the function on a picture is 4 → point (0, 4).

y-intercept for the function

is for x = 0. substitute:

y-intercept is 8 → point (0, 8).