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?

Answers

  1. Answer:
      14400 cm³/s
    Step-by-step 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

Leave a Comment