Chapter 13 - Partial Derivatives - 13.3 Partial Derivatives - Exercises Set 13.3 - Page 938: 59

(a) dV/dr= 2πrh (b) dV/dh = πr^2 (c) 48π (d) 64π

(a) Instantaneous rate of change d(πr^h)/dr= π(2r)h= 2πrh (b) If r remains constant, instantaneous rate of change d(πr^2h)/dh= πr^2 (c) Given, h=4in and r=6in From (a) we get dV/dr= 2πrh = 2π*(6)*(4) = 48π (d) Given, h=10in and r=8in From (b) we get, dV/dh = πr^2 = π(8)^2 =64π