At a certain instant the edge of a cube is 7 inches long and the volume is increasing at the rate of 3 cubic inches per minute. How fast is the surface area of the cube increasing

The surface area increases at 12/7 square inches per minute

Step-by-step explanation:

Given

--- side length

--- Rate at which volume increases

Required

The rate at the area

The volume of a cube is:

Differentiate with respect to time

When and

The expression becomes:

Divide both sides by 3

Divide both sides by 49

The surface area is calculated as:

Differentiate with respect to time

Substitute: and

The surface area increases at 12/7 square inches per minute