If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at which the diameter decreases when the diameter is 10 cm.

The diameter decreases at a rate of -0.0477 cm/min when it is 10 cm.

Step-by-step explanation:

Surface area of a snowball:

A snowball has a spheric format, which means that it's surface area is given by:

In which r is the radius, which is half the diameter. In function of the diameter, the area is given by:

Solving the question:

To solve this question, we have to implicitly derivate the area in function of t. So

Snowball melts so that its surface area decreases at a rate of 3 cm2/min

This means that

Find the rate at which the diameter decreases when the diameter is 10 cm.

This is when . So

The diameter decreases at a rate of -0.0477 cm/min when it is 10 cm.

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step-by-step explanation: