Question

The edges of a cube increase at a rate of 3 cm/s. How fast is the volume changing when the length of each edge is 40 cm?

Answer 1

14400 cm³/s

Explanation:

Find the rate of change of volume in terms of edge length, and evaluate the expression for the given conditions.

Rate of change of volume

V = s³ . . . . volume in terms of edge length (s)

dV/dt = 3s²·ds/dt . . . . . . derivative of volume with respect to time

For the given values of s and ds/dt, this is ...

dV/dt = 3(40 cm)²(3 cm/s) = 14400 cm³/s