# Related Rates

• Mar 10th 2010, 07:50 PM
rhcp1231
Related Rates
As a circular griddle is being heated, its diameter changes at a rate of 0.01 cm/min. When the diameter is 30 cm, at what rate is the area of the griddle changing?

I know my formula is V=PI*r^2
and i know since i am given a diameter i would use (h/2) for my radius.

but once i take my derivative of the area formula and plug in my diameter and my DD/DR as .01 cm/min, i am given .942...

what am i doing wrong?
• Mar 10th 2010, 08:10 PM
Jhevon
Quote:

Originally Posted by rhcp1231
As a circular griddle is being heated, its diameter changes at a rate of 0.01 cm/min. When the diameter is 30 cm, at what rate is the area of the griddle changing?

I know my formula is V=PI*r^2
and i know since i am given a diameter i would use (h/2) for my radius.

but once i take my derivative of the area formula and plug in my diameter and my DD/DR as .01 cm/min, i am given .942...

what am i doing wrong?

Your formula is: $A = \pi r^2 = \frac {\pi D^2}4$

And so, by differentiating implicitly with respect to time, you get: $\frac {dA}{dt} = \frac {\pi D}2 \cdot \frac {dD}{dt}$

Now, you want $\frac {dA}{dt}$ when $D = 30$ and $\frac {dD}{dt} = 0.01$, just plug those in and compute.
• Mar 10th 2010, 08:13 PM
rhcp1231
Quote:

Originally Posted by Jhevon
Your formula is: $A = \pi r^2 = \frac {\pi D^2}4$

And so, by differentiating implicitly with respect to time, you get: $\frac {dA}{dt} = \frac {\pi D}2 \cdot \frac {dD}{dt}$

Now, you want $\frac {dA}{dt}$ when $D = 30$ and $\frac {dD}{dt} = 0.01$, just plug those in and compute.

it was so obvious lol thanks man