Calculus for enginerring

Question

The lengths p,q,r of the edges of a rectangular box are changing with time. At the instant p=2m,q=3m,r=4m dp/dT=dQ/dt=1m/sec and dr/dt=2m/sec. At what rate is the box's volume v changing at that instant?

Answer 1

V = pqr

dV/dt = (pq)dr/dt + (pr)dq/dt + (qr)dp/dt = 12 + 8 + 12 = 32 m³/sec