The volume of a cube is increasing at the rate of 8 cm³/s. How fast is the surface area increasing when the length of an edge is 12 cm?

The volume of a cube is increasing at the rate of 8 cm³/s. How fast is the surface area increasing when the length of an edge is 12 cm?

• A. 4/3 cm²/s
• B. 2 cm²/s
• C. 8/3 cm²/s
• D. 8 cm²/s

Answer: C) 8/3 cm²/s

Explanation: V = x³. dV/dt = 3x²(dx/dt) = 8, so dx/dt = 8/(3x²). Surface area S = 6x². dS/dt = 12x(dx/dt) = 12x(8/(3x²)) = 32/x. When x = 12, dS/dt = 32/12 = 8/3 cm²/s.