Question

The volume of a cube is increasing at the rate 18cm^3/sec. how fast is an edge measuring 2 cm expanding ?

Answer 1

EXPLANATION

Given that the increasing rate is 18cm^3/s, we can apply the following realtionship:

`dV/dt=18`

As the volume is equal to the multiplication of the sides and assuming that the edge is called "x" we have:

`dV/dt=d(x^3)/dt\cdot d/dx`

Applying derivatives:

`dV/dt=3x^2(dx)/(dt)=18`

Isolating dx/dt:

`dx/dt=18/3x^2`

Therefore:

`dV_{\text{ }}/dt=(18)/(3x^2)=(6)/(x^2)`

Now, if the measure of the edge is 2cm, we can plug this number into the velocity equation to obtain the speed:

Hence, the speed is 1.5 cm/s