The volume of a rectangular box with a square base remains constant at 500 cm3 as the area of the base increases at a rate of 10 cm2/sec. Find the rate at which the height of the box is decreasing when each side of the base is 19 cm long. (Do not round your answer.)

The rate of change of the height of the box at which is decreasing is centimeters per second.

Step-by-step explanation:

From Geometry the volume of a rectangular box (), measured in cubic centimeters, with a square base is modelled by the following formula:

(Eq. 1)

Where:

- Area of the base, measured in square centimeters.

- Height of the box, measured in centimeters.

The height of the box is cleared within the formula:

If we know that and , then the current height of the box is:

The rate of change of volume in time (), measured in cubic centimeters per second, is derived from (Eq. 1):

(Eq. 2)

Where:

- Rate of change of the area of the base in time, measured in square centimeters per second.

- Rate of change of height in time, measured in centimeters per second.

If we get that , , and , then the equation above is reduced into this form:

Then, the rate of change of the height of the box at which is decreasing is:

The rate of change of the height of the box at which is decreasing is centimeters per second.

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