All wedges of a cube are expanding at a rate of 6 cm/sec .How fast is the surface area changing when each edge is (a) 2 cm and (b) 10cm

Answer 1

Let c=length of each side,
Area of cube, A = 6c²
Rate of change of area with respect to side = dA/dc = 12c
Rate of change of Area can be found by the chain rule,

dA/dt
= dA/dc * dc/dt
= 12c * 6 cm/s
=72c cm/s ...(1)
(a) c=2 cm,
(b) c=10 cm
Substitute values of c in expression (1) to get the rate of change of area with respect to time.