related rate problem

**hazecraze** · October 28th 2009, 05:18 PM

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 $r^2$

relating diameter(x) to radius:
$2r=x, r=\frac{x}{2}$

$\frac{ds}{dt}=2$ 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

.

**skeeter** · October 28th 2009, 05:39 PM

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 $r^2$

relating diameter(x) to radius:
$2r=x, r=\frac{x}{2}$

$\frac{ds}{dt}=2$ 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

.

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

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