The surface area is changing at a rate of 540 cm²/second
Let 'a' be the length of each edge of a cube.
A cube has a total of 12 edges with equal length.
Rate of change of the expansion of the edge, da/dt = 5 cm/second
Area of one face of a cube = a²
A cube has 6 faces. So,
The surface area of a cube, S = 6a²
Rate of change of surface area,
dS/dt = 6 x 2a x (da/dt)
⇒ dS/dt = 12a x 5
When a = 9 cm,
the rate of change of surface area of the cube = 60 x 9
= 540 cm²/second
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