The volume of a cube increases by 2.0 m^3 / s, With what speed does the cube's side changes when the side is 6.0 m?

Thx for any help I can get here!

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- Jun 7th 2012, 01:15 AMAiylaCalculate the side of the cube
The volume of a cube increases by 2.0 m^3 / s, With what speed does the cube's side changes when the side is 6.0 m?

Thx for any help I can get here! - Jun 7th 2012, 01:50 AMbiffboyRe: Calculate the side of the cube
- Jun 7th 2012, 01:55 AMSarasijRe: Calculate the side of the cube
I hope you know basic calculus. I am answering your question with it.

Let the volume and a side of a cube be V m^{3}& a m. respectively.

So, V=a^{3}

Now differentiate both sides with respect to time t.

i.e. dV/dt = 3a^{2}da/dt

We have to find da/dt while a=6 & we know dV/dt=2.

i.e. 2 = 3 x 6^{2}x da/dt.

or, da/dt = 2/(3 x 36) = 1/54 m/s. - Jun 13th 2012, 10:15 PMrichard1234Re: Calculate the side of the cube
We know that $\displaystyle V = L^3$. Differentiating both sides with respect to time t,

$\displaystyle \frac{dV}{dt} = 3L^2 \frac{dL}{dt}$

Particularly, when $\displaystyle \frac{dV}{dt} = 2 \frac{m^3}{s}$ and $\displaystyle L = 6 m$,

$\displaystyle \frac{dL}{dt} = \frac{1}{54} \frac{m}{s}$