The edge of a cube is increasing at a rate of 7 cm/s. The rate of cha…

The correct answer is Option (4) → 252 cm²/s

Let the edge be x cm at time t. The area of a cube means its total surface area, made up of 6 square faces:

    \(A = 6x^2\)

Differentiating with respect to t (chain rule):

    \( \displaystyle \frac{dA}{dt} = 12x\,\frac{dx}{dt} \)

Putting \(x = 3\) and \(\frac{dx}{dt} = 7\):

    \( \displaystyle \frac{dA}{dt} = 12 \times 3 \times 7 = 252 \text{ cm}^2/\text{s} \)