Answer:
dh/dt = 0,111 cm/min
Step-by-step explanation:
Volume of the rectangular box is:
V = V(b) = Area of the rectanglar base * height
Area of the base is : 3*2 = 6 cm²
V(b) = 6*h
Differentiating in relation to time in both sides of the equation give:
d(V(b))/ dt = 6* dh/dt (1)
According to problem statement volume of the box is decreasing at the rate of 2 cm each 3 min then by rule of three
2 cm ⇒ 3 min
x ⇒ 1 min
x = 2/3 = 0,67 cm/min
As dimensions of the box ( length and width ) will be constants decreasing in the volume of the cube does not depend on the level of the height, and we know dV(b) / dt = 0.67 cm/min, then in equation 1
0.67 = 6*dh/dt
dh/dt = 0.67/6
dh/dt = 0,111 cm/min
