How many #cm^3# in a #10*m^3# volume?

1 Answer
Feb 19, 2016

Answer:

#1# #cm^3# #=# #1xx(10^-2*m)^3#. There are thus #10^7# #cm^3# in a #10# #m^3# volume.

Explanation:

The #"centi"# prefix means #10^-2#.

So #1# #cm^3# #=# #(1xx10^-2*m)^3# #=# #(1xx10^-2*mxx1xx10^-2*mxx1xx10^-2*m)##=# #1xx10^-6*m^3#.

Thus there are 1 million #cm^3# in a cubic metre. Do you agree? All I have done is expanded the prefix #"centi"# using the cubic exponent. Since, there are #1# #million# #cm^3# in a cubic metre, there are #10xx10^7# #cm^3# in a #10# #m^3# volume.

The conversion factor is #10^6# #cm^3m^-3#