The surface area of cube is growing at a constant rate of 54 ft^2/min. What is the rate of change of the volume of the cube when the cube has side length 20?

Question

jack1 · Answer

do u understand (mathematically) the relationship between volume and surface area?

irishboy123 · Answer

$A = 6 x^2 \
\dot A = 12 x \; \dot x$

$V = x^3$
$\dot V = 3 x^2 \; \dot x = \dots$

jmartinez638 · Answer

*A little confused*

irishboy123 · Answer

are you learning/applying calculus?

jmartinez638 · Answer

I am learning calculus, but I'm not so so far into it. Just touching related rates and need help working through this problem

irishboy123 · Answer

the chain rule seems important here.  you know that?

$\dfrac{dy}{dt} = \dfrac{dy}{dx}\dfrac{dx}{dt}$

jmartinez638 · Answer

yes

irishboy123 · Answer

and $A = 6 x^2 $ should make great sense too

as $\dfrac{ dA}{dt} = \dfrac{dA}{dx} \dfrac{dx}{dt} = 12 x \; \dfrac{ dx}{dt} $

irishboy123 · Answer

"as" :-((

so

jmartinez638 · Answer

Ah, that makes sense. Thanks