If a snowball melts so that its surface area decreases at a rate of 5 cm2/min, find the rate (in cm/min) at which the diameter decreases when the diameter is 9 cm

0.0221 cm/min

Step-by-step explanation:

Surface area of a snowball:

An snowball has a spherical format.

The surface area of an sphere is given by:

In which r is the radius(half the diameter). So in function of the diameter, we have that:

Implicit derivative:

To solve this question, we need to find the implicit derivative of A in function of t.

The variables are A and d, so:

Its surface area decreases at a rate of 5 cm2/min

This means that

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

This is when . So

This means that the diameter decreases at a rate of 0.0221 cm/min when the diameter is 9 cm.

*face palms*

step-by-step explanation:

no