Question

The edges of a cube shrink at a rate of 2 centimeters per second. What is the
rate of change of the surface area of the cube when the sides have length 3 centimeters?

Answer 1

Let the side of cube be a

here,

da/dt = 2 cm/s

now,

let the Area be A

surface area of cube = A

where.

A = 6a²

so,

Rate of shrinking of surface area = dA/dt

= 12a per sec

given side = 3 cm

so,

rate of shrinking of surface area = 12(3) = 36²cm/s