Answer :
Answer:
a) V' = 81(1)^2 = 81 cm^3/s
b) V' = 81(10)^2 = 8,100 cm^3/s
Step-by-step explanation:
Recall that the volume of a cube is:
V = s^3
If you let t be the time in a seconds, then s = 3t at time t. So we have that the volume of the cube at time t is:
V = (3t)^3 = 27t^3
Taking derivatives:
V' = 81t^2
Then, the speed of which the volume changes is:
a) V' = 81(1)^2 = 81 cm^3/s
b) V' = 81(10)^2 = 8,100 cm^3/s