Volume of a cube????

Question

All edges of a cube are expanding at a rate of 3 centimeters per second. How fast is the volume changing when each edge is A)1 centimeter and B)10 centimeters.

Thanks

Answer 1

volume of a cube is given by  vol = a^3

  differentiating it w.r.t time u get

  dv/dt = 3*a^2*da/dt

now since u r given  da/dt as 3cm/sec

u get

  dv/dt  =  9*a^2

now when  

A)   a=1cm

    dv/dt  = 9cm^3/sec

B)   a=10

    dv/dt  =  900cm^3/sec

Answer 2

A  63 cm3 per second  (4 * 4* 4) - (1 * 1 * 1)

B  1197 cm3 per second (13 * 13 * 13) - (10 * 10 * 10)

Answer 3

rate of change of the volume is 3X^2

so 3, and 300 cm/s