If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate (in cm/min) at which the diameter decreases when the diameter is 9 cm. (Round your answer to three decimal places.)

The diameter decreases at a rate of 0.053 cm/min.

Step-by-step explanation:

Surface area of an snowball

The surface area of an snowball has the following equation:

In which d is the diameter.

Implicit differentiation:

To solve this question, we differentiate the equation for the surface area implictly, in function of t. So

Surface area decreases at a rate of 3 cm2/min

This means that

Tind the rate (in cm/min) at which the diameter decreases when the diameter is 9 cm.

This is when . So

The diameter decreases at a rate of 0.053 cm/min.

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step-by-step explanation:

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