## angelarios 2 years ago all edges of a cube are expanding at a rate of 3 centimeters per second. how fast is the volume changing when each edge is (a) 1 cm. (b) 10 cm.

1. satellite73

looks like a related rate problem fortunately the formula for the volume of a cube is easy, it is $$V(x)=x^3$$

2. satellite73

take the derivative with respect to time and get $V'=3x^2x'$

3. satellite73

you are told $$x'=3$$ so this is really $V'=9x^2$ replace $$x$$ by the various values to get $$V'$$

4. angelarios

dV/dt=9x^2dx/dt ?:)

5. satellite73

no

6. satellite73

i used $$V'$$ and $$x'$$ instead of $$\frac{dV}{dt}$$ and $$\frac{dx}{dt}$$ because it was easier for me to write also for you it is easier

7. satellite73

but in your notation, you have $V=x^3$ so $\frac{dV}{dt}=3x^2\frac{dx}{dt}$

8. satellite73

this line all edges of a cube are expanding at a rate of 3 centimeters per second tells you that $$\frac{dx}{dt}=3$$

9. satellite73

that means $$\frac{dV}{dt}=3x^2\times 3=9x^2$$

10. satellite73

let me know if i lost you there

11. angelarios

Ok got it(:

12. angelarios