Question

The volume of a cube is increasing at the rate of 8 cm3 / sec. How fast is the surface area increasing when the length of an edge is 12 cm ?

Answer 1

Let x, v, * be length of the edge, volume and surface area of the cube respectively.

Given x = 12 cm.

dv/dt = 8 cm3 /sec.

We know v = x3

dv/dt = 3x2 dx/dt

⇒ dx/dt = 1/3x2 dv/dt

= (1/3.12.12).8 = 1/54

• = 6x2

ds/dt = 6.2x.dx/dt

= 6.2.12.(1/54) = 8/3 cm2 /sec

∴ Surface area increasing at the rate of 8/3 cm2 /sec.