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? March 21, 2023 by Thiên Hương 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: 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 Reply
Rate of change of volume