The volume of a cube is increasing at a rate of 9 cm³/s. The rate at which the surface area is increasing when the side is 2 cm is:

The volume of a cube is increasing at a rate of 9 cm³/s. The rate at which the surface area is increasing when the side is 2 cm is:

• A. 6 cm²/s
• B. 12 cm²/s
• C. 9 cm²/s
• D. 18 cm²/s

Answer: A) 6 cm²/s

Explanation: V = x³, dV/dt = 3x² dx/dt = 9 → 3(4) dx/dt = 9 → dx/dt = 3/4. S = 6x², dS/dt = 12x dx/dt = 12(2)(3/4) = 18 cm²/s. Option D is 18, so correct index is 3.