A spherical snowball is melting in such a way that its diameter is decreasing at rate of 3 cm/min. At what rate is the volume of the snowball decreasing when the diameter is 11cm?
When the diameter is 11cm, the volume of the snowball is decreasing at a rate of _______ .
I know that the volume of a sphere is . So I use implicit differentiation and take the derivative of both sides and use the chain rule because I know is a function of , and I believe this rate is given as -3, so .
Since the radius of a circle is one half the diameter... , however, this answer is incorrect.
I was given a hint that I have to write an equation linking the changing volume V(t) to the changing diameter d(t), where
I don't understand how to figure this out. Also, I don't have the answer so please don't give it to me. Thanks in advance.