V= π/3 (x^2+y^2+xy)z
(π = pi)
it is given that dx/dt = 2 dy/dt = 3 and dz/dt = 1.5
and finding the volume when x = 10, y =16 and z =8
I got dv/dt = 786π
can any 1 please do this and check if its right please
V = pi/3 (x^2 + y^2 + xy)z
=> V= pi/3 (zx^2 + zy^2 + xyz)
=> dV/dt = pi/3 (x^2 dz/dt + 2xz dx/dt + y^2 dz/dt + 2yz dy/dt + xy dz/dt + zy dx/dt + xz dy/dt)
=> dV/dt = pi/3 [(2xz + zy)dx/dt + (2yz + xz)dy/dt + (x^2 + y^2 + xy)dz/dt]
When x = 10, y =16, z =8, dx/dt = 2 dy/dt = 3 and dz/dt = 1.5
=> dV/dt = pi/3 {[2(10)(8) + (8)(16)](2) + [2(16)(8) + (10)(8)](3) + [(100) + (256) + (10)(16)](1.5)}
=> dV/dt = pi/3 (576 + 1008 + 774)
=> dV/dt = pi/3 (2358)
=> dV/dt = 786 pi
You were right! (Unless, of course, we're both wrong)