# related rate problem

• Oct 28th 2009, 05:18 PM
hazecraze
related rate problem
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.
• Oct 28th 2009, 05:39 PM
skeeter
Quote:

Originally Posted by hazecraze
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.

Did it a little differently, but I get the same solution.