Expansion problem

**jimmyp** · June 11th 2009, 08:36 PM

All edges of a cube are expanding at a rate of 3cm per second. How fast is the surface area changing when each edge is (a) 1cm and (b) 10 cm?

Not sure how to approach the probme.

**alexmahone** · June 11th 2009, 09:06 PM

$S=6a^2$
$\frac{dS}{dt}=6*2a\frac{da}{dt}$

$\frac{da}{dt}=3 cm/sec$

$\frac{dS}{dt}=6*2a*3$
$\frac{dS}{dt}=36a$

a) $\frac{dS}{dt}=36*1=36 cm^2/sec$

b) $\frac{dS}{dt}=36*10=360 cm^2/sec$

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