The volume of a cube is increasing at a rate of 10 cm^3/min. How fast is the surface area increasing when the length of an edge 90 cm?

1 Answer
May 24, 2018

1227 cms squared per minute.

Explanation:

Let the length of a side of the cube =x

Then volume of cube v =x3.........[1]
Surface area of cube s will = 6x2......[2]

Differentiating [1] implicitly w.r.t. t[ time], dvdt=3x2dxdt , but we know from the question that dvdt=10, therefore dxdt=103x2......[3]

Differentiating.......[2] w.r.t. t, dsdt=12xdxdt and substituting for dxdt from .....[3] we obtain,

dsdt=[12x103x2] = 1203x, and so we have the rate of change of the side length of the cube with respect to time, and when x=90, dsdt=1203[90] = 1227.

Hope this was helpful.