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.
$\displaystyle S=6a^2$
$\displaystyle \frac{dS}{dt}=6*2a\frac{da}{dt}$
$\displaystyle \frac{da}{dt}=3 cm/sec$
$\displaystyle \frac{dS}{dt}=6*2a*3$
$\displaystyle \frac{dS}{dt}=36a$
a) $\displaystyle \frac{dS}{dt}=36*1=36 cm^2/sec$
b) $\displaystyle \frac{dS}{dt}=36*10=360 cm^2/sec$