# Thread: Calculate the side of the cube

1. ## Calculate 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!

2. ## Re: Calculate the side of the cube

Originally Posted by Aiyla
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!
We are given dV/dt = 2.0 We want dL/dt (L is length of side) Use dL/dt = dV/dt*dL/dV V=L^3 dV/dL =3L^2 So dL/dV = 1/(3L^2)

3. ## Re: Calculate the side of the cube

Originally Posted by Aiyla
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!
I hope you know basic calculus. I am answering your question with it.

Let the volume and a side of a cube be V m3 & a m. respectively.

So, V=a3

Now differentiate both sides with respect to time t.

i.e. dV/dt = 3a2da/dt

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

i.e. 2 = 3 x 62 x da/dt.

or, da/dt = 2/(3 x 36) = 1/54 m/s.

4. ## Re: 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 $\displaystyle L = 6 m$,

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