Answer:
The volume of the cube is decreasing at a rate of 63.1071 cubic millimeters per minute.
Step-by-step explanation:
The volume of a cube is given by:
[tex]V=s^3[/tex]
Implicitly differentiate the equation with respect to time t:
[tex]\displaystyle \frac{dV}{dt}=3s^2\frac{ds}{dt}[/tex]
The edge of the cube decreases by 0.53 mm/min. Therefore, ds/dt = -0.53.
When the edge is 6.3 mm, s = 6.3.
Substitute and evaluate:
[tex]\displaystyle \frac{dV}{dt}=3(6.3)^2\left(-0.53\right)=-63.1071\text{ mm}^3/\text{min}[/tex]
The volume of the cube is decreasing at a rate of 63.1071 cubic millimeters per minute.
