An edge of a variable cube is increasing at a rate of . How fast the volume of the cube will increase when the edge is long.
Step 1. Given data:
The variable edge of the cube,
The edge of the cube,
Step 2. Formula used:
The volume of the cube,
Step 3. Finding the increase in the volume of the cube:
Differentiating both sides of the equation , we get
Hence, the volume of the cube is increasing at the rate of
Hence, option A is correct.