If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at which the diameter decreases when the diameter is 12 cm. (Give your answer correct to 4 decimal places.)
$\displaystyle \frac{ds}{dt}=-3$
$\displaystyle d=12$
$\displaystyle S=4$π$\displaystyle r^2$
relating diameter(x) to radius:
$\displaystyle 2r=x, r=\frac{x}{2}$
$\displaystyle \frac{ds}{dt}=2$π$\displaystyle x\frac{dx}{dt}$
$\displaystyle -3=2$π$\displaystyle (12)\frac{dx}{dt}$
$\displaystyle \frac{dx}{dt}=\frac{-3}{24pi}$
=-.039788
to 4 decimal places, $\displaystyle -.0398$
I got the http://www.webassign.net/wastatic/common/img/cross.png.
