All edges of a cube are expanding at a rate of 3 cm/s. How fast is the volume changing when the length of each edge is 50 cm?

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

i think it would be 42cm