Question

A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.2 cm/min. at what rate is the volume of the snowball decreasing when the diameter is 13 cm

Answer 1

dd/dt = -0.2 cm/min
d = 10 cm

Next, you need to know the volume formula for a sphere.

V = 4πr³ / 3

The last piece of information you need to know is that the diameter is twice the radius (should already know this). Rewrite the equation in terms of diameter.

V = 4π(d/2)³ / 3

Now we can take the derivative of the equation with respect to time t. (Note that "dd/dt" means "the derivative of the diameter with respect to time".)
dV/dt = (1/3)(4π)(1/8)(3d²)(dd/dt)

Substitute in everything that you know.
dV/dt = (1/3)(4π)(1/8)(3(10)²)(-0.2)

Now just multiply everything to get the decrease in volume with respect to time.
dV/dt = -31.416 cm/min <= FINAL ANSWER

You're answer was only wrong because you forgot the negative sign (its diameter is decreasing and so is the volume). I hope this helped.