The surface area of a cube is increasing at a rate of 15 square meters per hour. At a certain instant, the surface area is 24 square meters. What is the rate of change of the volume of the cube at that instant (in cubic meters per hour)?

The volume of cube is increasing at a rate 7.5 cubic meter per hour.  

Step-by-step explanation:

We are given the following in the question:

Surface area of cube = 24 square meters.

Let l be the edge of cube.

Surface area of cube =

Thus, at that instant the edge of cube is 2 meters.

We have to find the rate of change in volume.

Volume of cube =

Rate of change of volume =

Thus, the volume of cube is increasing at a rate 7.5 cubic meter per hour.

you need to rotate this triangle about the origin 270 degrees clockwise to create the full square.