# 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.)
$\frac{ds}{dt}=-3$

$d=12$

$S=4$π $r^2$

$2r=x, r=\frac{x}{2}$

$\frac{ds}{dt}=2$π $x\frac{dx}{dt}$

$-3=2$π $(12)\frac{dx}{dt}$

$\frac{dx}{dt}=\frac{-3}{24pi}$

=-.039788
to 4 decimal places, $-.0398$
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.)
$\frac{ds}{dt}=-3$

$d=12$

$S=4$π $r^2$

$2r=x, r=\frac{x}{2}$
$\frac{ds}{dt}=2$π $x\frac{dx}{dt}$
$-3=2$π $(12)\frac{dx}{dt}$
$\frac{dx}{dt}=\frac{-3}{24pi}$
to 4 decimal places, $-.0398$