A metal cube dissolves in acid such that an edge of the cube

A metal cube dissolves in acid such that an edge of the cube decreases by 0.70 mm/min. How fast is the volume of the cube changing when the edge is 8.60 MM? The volume is changing at a rate of _mm^3/mi

Solution

let length of side of metal cube= x

volume v =x³

differentiate with respect to time t

dv/dt =3x² dx/dt

x =8.6 mm , dx/dt =0.7 mm/min

dv/dt =3*8.6² *0.7

dv/dt =155.316

The volume is changing at a rate of 155.316 mm^3/min