Question

The edges of a cube are expanding at a rate of 5 centimeters per second. How fast is the surface area changing when the volume reaches 729 cubic centimeters?

a) 3 cm²/s
b) 4 cm²/s
c) 5 cm²/s
d) 6 cm²/s

Answer 1

The surface area is changing at a rate of 6 cm²/s when the volume reaches 729 cubic centimeters.

Step-by-step explanation:

To find how fast the surface area is changing when the volume reaches 729 cubic centimeters, we need to relate the volume and surface area of a cube. The volume of a cube is given by V = s^3, where s is the length of the side. The surface area of a cube is given by SA = 6s^2.

Since we are given that the edges of the cube are expanding at a rate of 5 centimeters per second, we can differentiate both the volume and surface area equations with respect to time, t.

Now, we can substitute the given values for s and the rate at which s is changing into the equations to find the rate at which the volume and surface area are changing. When the volume reaches 729 cubic centimeters, the surface area is changing at a rate of 6 cm²/s (option d).