If a snowball melts so that its surface area decreases at a rate of $1\ cm^2/min$, find the rate at which the diameter decreases when the diameter is 10 cm.
So I know that the surface area of a sphere is $A = 4\pi r^2$, $ds / dt = -1$, and we are trying to find $dd/dt$
I tried the following but got a wrong answer. Not sure where I made my mistake. Can someone clarify where I made a mistake? $$ ds/dt = 4 \pi r^2 (dd/dt) \\ -1 = 8 \pi r^2 (dd/dt) \\ -1/8 \pi(10/2) = dd/dt \\ = -0.00795 $$
it seems that actually you are finding the rate of change of the radius. We can rewrite the equation of the surface area as follows:
$A = 4\pi (d/2)^{2}$
If we differentiate implicitly with respect to t, we will then get that:
$\displaystyle\frac{dA}{dt} = 2\pi d \displaystyle\frac{dd}{dt}$
Clearing out the terms gives that the answer is $\approx -0.0159$.