A spherical snowball is placed in the sun. The snowball melts so that it's surface area

decreases at a rate of 2 cm2
/min. Find the rate at which the diameter decreases when the
diameter is 8 cm.

I'm not sure what formulas to use, SA and/or Volume. And im not sure how to calculate it.

To solve this problem, we need to use the formulas for the surface area and volume of a sphere along with the concept of rates of change.

Let's start by finding the formula for the surface area of a sphere. The surface area (SA) of a sphere with radius r is given by:

SA = 4πr²

Next, let's find the formula for the volume of a sphere. The volume (V) of a sphere with radius r is given by:

V = (4/3)πr³

In this problem, we are given that the surface area decreases at a rate of 2 cm²/min. Let's denote the rate of change of the surface area as dSA/dt.

We need to find the rate at which the diameter decreases when the diameter is 8 cm. Since the diameter (d) of a sphere is twice the radius (r), we can express the diameter in terms of r as:

d = 2r

We are interested in finding the rate of change of the diameter with respect to time (dt), which can be written as dd/dt.

To solve for dd/dt, we can differentiate the equation d = 2r with respect to time:

dd/dt = 2(dr/dt)

Now, we need to relate the rate of change of the diameter (dd/dt) to the rate of change of the surface area (dSA/dt). We know that the surface area is related to the radius as SA = 4πr². Differentiating this equation with respect to time, we get:

dSA/dt = 8πr(dr/dt)

Substituting the given value of dSA/dt = -2 cm²/min (negative sign indicates the decrease), we have:

-2 = 8πr(dr/dt)

We need to find the rate of change of the diameter when the diameter is 8 cm, so we substitute d = 8 cm and r = 4 cm into the equation:

-2 = 8π(4)(dd/dt)

Simplifying the equation, we find:

dd/dt = -2/(32π) cm/min

Therefore, the rate at which the diameter decreases when the diameter is 8 cm is approximately -0.0199 cm/min.

who cares about the volume?

A = πd^2
dA/dt = 2πd dd/dt

Now plug in your numbers to find dd/dt