Question

The volume of a cube is increasing at a rate of 9 cubic centimetres per
second. How fast is the surface area increasing when the length of an edge is 10
centimetres ?

Answer 1

@terenzreignz @Shannon20150 @Noemi95

Answer 2

If we let S = the surface area, then we need to find...
\[\huge \frac{dS}{dt}\]
given of course that
\[\Large \frac{dV}{dt}=9\]

Answer 3

There he gave it to u

Answer 4

It would be nice if we could express S in terms of V

Answer 5

@terenzreignz's smart self got it gofor! (:

Answer 6

Meanwhile, @terenzreignz ' childish self is still sleeping, while his hungry self is indulging in ice cream...
:)

If we let x = one edge of the cube, then
\[\Large S = 6x^2\\\Large V=x^3\]

Answer 7

\[\huge \frac{dS}{dV}=\frac{\frac{dS}{dx}}{\frac{dV}{dx}}\]

Answer 8

\[\huge \frac{dS}{dt}=\frac{dS}{dV}\cdot\frac{dV}{dt}=\frac{\frac{dS}{dx}\times \frac{dV}{dt}}{\frac{dV}{dx}}\]

Answer 9

Thankyou Sir

Answer 10

And then, plug in x = 10

Answer 11

HELP http://openstudy.com/study#/updates/517df6f6e4b0be6b54ab6738