Question

a rectangular room is 20 ft by 12 ft by 8 ft. If the length is decreasing by 4 inches per minute, the width is decreasing by 5 inches per minute and the height remains constant, how fast is the volume changing after 2 minutes?

Answer 1

let the width be x
let the length be y
let the height be h

V= xyh
dV/dt = xy dh/dt + xh dy/dt + yh dx/dt

given x=20, y=12, h = 8
dx/dt = 5
dy/dt = -4
dh/dt = 0

Plug in those values into dV/dt