Question

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 is 3.0 cm?

Answer 1

Answer:

Surface area of the cube is increasing at a rate of 49 cm2min

Explanation:

If the length of an edge of a cube is l cm.,

its volume V is l3 and surface area A is 6l2.

Differentiating V=l3 w.r.t. time, we get

dVdt=3l2dldt

As dVdt=10 cm3min, wen l=90

dldt=103×902=12430

As A=6l2

dAdt=12l×dldt=12×90×12430=49 cm2min

Answer 2

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