Question

The edge of a cube is increasing at the rate of 0.05 cm/sec. In terms of the edge of cube (s), what is the rate of change of the volume of the cube, in cm^3/sec?

Answer 1

Let edge of cube=xcm
dx/dt=0.05 cm/sec.
Let V be the volume
v=x^3 cm^3
dv/dt=3x^2 dx/dt=3x^2*0.05=0.15x^2 cm^3
If x is given then substituting we can find dv/dt i.e,rate of change of volume.

Answer 2

Thanks, I had no idea where to even start with this.
x=s in this problem, so plugging that in, I got .15s^2, which is the correct answer according to the answer key.