Question

All the edges of a cube are decreasing at a rate of 6cm per second.

a. How fast is the volume changing when each edge is 10cm?

b. How is the surface area changing at the same instant?

Answer 1

ds/dt=-6cm/sec
a) V=s^3
dV/dt=3s^2*ds/dt
dV/dt=3*100*(-6)
dV/dt=-1800cm/sec

b) SA=6s^2
dSA/dt=12s*ds/dt
dSA/dt=12*10*(-6)
dSA/dt=-720cm/sec

hope it helped

Answer 2

Thank you so much! Really helped. :)