Final answer:
The rate of change of the volume of a cube is found using related rates in calculus. With edges expanding at 3 cm/s and each edge at 10 cm, the volume changes at a rate of 900 cm³/s. This signifies how quickly the cube's volume is increasing under the specified conditions.
Step-by-step explanation:
This is asking about how quickly the volume of a cube changes as its edges expand at a constant rate. To find the rate of change of volume, we would use differential calculus, specifically related rates. For a cube with edges of length L, the volume V is given by V = L³. If the edges are expanding at 3 centimeters per second, we can denote the rate of change of the edge length as dL/dt = 3 cm/s. To find the rate of change of volume at the moment when each edge is 10 centimeters, we use the chain rule to relate dV/dt and dL/dt: dV/dt = d(L³)/dt = 3L² × (dL/dt). Plugging in the given values: dV/dt = 3 × (10 cm)² × (3 cm/s) = 900 cm³/s. So, the volume of the cube is changing at a rate of 900 centimeters cubed per second when each edge is 10 centimeters.