Question

The volume of a cube is 125 cm³, and it is changing at a rate of 8 cm³. How fast is the surface area changing at that moment?

a) 2 cm²/s
b) 4 cm²/s
c) 6 cm²/s
d) 8 cm²/s

Answer 1

The rate of change of the surface area of a cube can be found using the formula d(SA)/dt = 2 * √(V * dV/dt). Substituting the given values, we find that the surface area is changing at a rate of 20 cm²/s.

Step-by-step explanation:

To find the rate at which the surface area is changing, we can use the formula:

d(SA)/dt = 2 * √(V * dV/dt)

where d(SA)/dt is the rate of change of surface area, V is the volume of the cube, and dV/dt is the rate of change of the volume.

Given that V = 125 cm³ and dV/dt = 8 cm³, we can substitute these values into the formula:

d(SA)/dt = 2 * √(125 * 8) = 2 * 10 = 20 cm²/s

Therefore, the surface area is changing at a rate of 20 cm²/s at that moment.