# Thread: Calculus applications

1. ## Calculus applications

Each edge of a cube is expanding at a rate of 4cm/s. How fast is the volume changing when each edge is 5cm? At what rate is the surface area changing when each edge is 7 cm?

2. Originally Posted by mathamatics112
Each edge of a cube is expanding at a rate of 4cm/s. How fast is the volume changing when each edge is 5cm? At what rate is the surface area changing when each edge is 7 cm?
$\displaystyle \frac{dV}{dt} = (\frac{dV}{dr})(\frac{dr}{dt})$

$\displaystyle V = r^3$ and $\displaystyle \frac{dr}{dt} = 4cm.s^{-1}$

Can you go from there?

3. is that the equation i am using for the first one?

4. Originally Posted by mathamatics112
is that the equation i am using for the first one?
Note, I'm using r for any one side on the cube rather than a radius

Yeah, it's an application of the chain rule.

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2. As the surface area is $\displaystyle A = 6r^2$ and $\displaystyle \frac{dr}{dt} = 4cm.s^{-1}$

this will be $\displaystyle \frac{dA}{dt} =(\frac{dA}{dr})(\frac{dr}{dt})$