At time t is greater than or equal to zero, a cube has volume V(t) and edges of length x(t). If the volume of the cube decreases
at a rate proportional to its surface area, which of the following differential equations could describe the rate at which the volume of the cube decreases? A) dV/dt=-1.2x^2
B) dV/dt=-1.2x^3
C) dV/dt=-1.2x^2(t)
D) dV/dt=-1.2t^2
E) fav/dt=-1.2V^2
The rate of change of volume is given by dV/dt. Surface area is proportional to x^2. Since the volume is decreasing, the constant of proportionality between surface area and rate of volume change will be negative. Hence a possible equation might be ...
