The edge of a cube is increasing at a rate of 7 cm/s, so dtda=7 cm/s.
The edge length at this moment is a=3 cm.
A cube has 6 faces, each face is a square with area a2.
Surface Area A=6a2
Differentiating both sides with respect to time t:
dtdA=6×2a×dtda
dtdA=12a×dtda
Substituting a=3 cm and dtda=7 cm/s:
dtdA=12×3×7
dtdA=36×7
dtdA=252 cm²/s
Therefore, the rate of change of surface area of the cube is 252 cm²/s.