Video Transcript
How many cubic centimetres are in
0.02 cubic metres?
There are a couple of different
ways to answer this question. One is primarily in algebraic
way. And another is mostly a geometric
method. In the algebraic method, we start
out by recalling the conversion between metres and centimetres. One metre is equal to 100
centimetres. Then, what we do is cube both sides
of this equation, multiply each side by itself twice over. Once we’ve done this, it means we
can take any given value in cubic metres, say for example, the one we’re given in
this problem statement, 0.02 cubic metres. And then, we can replace the metres
cubed with 100 centimetres quantity cubed. And the reason we can do that is
because of the equality that we’ve just established over here. So 0.02 cubic metres is equal to
0.02 times the quantity, 100 centimetres cubed.
The next step is to cube both the
units as well as the number within the parentheses. 100 cubed is 1000000, a one
followed by six zeros. And centimetres cubed is cubic
centimetres. All we have to do then is multiply
this 1000000 cubic centimetres by 0.02. And when we do that, we find a
result of 20000 cubic centimetres. This then is our answer to the
question, 20000. But now, let’s look at that second
method, the geometric method, for finding this answer.
Another way to do this is to draw a
box and let the dimensions of this box fit certain values. What we’ll do is we’ll let the
height of the box be one metre, the width of the box be one metre. But the depth of the box we’ll let
be 0.02 metres. And you can see we haven’t chosen
this value by accident. That value matches the prefix in
0.02 cubic metres. Now, what is the volume 𝑉 of our
box? Well, it’s one metre times one
metre times 0.02 metres. In other words, it’s 0.02 metres
cubed. And what we want is to express this
volume in a different set of units, in cubic centimetres.
To find this value, let’s return to
our statement from earlier that one metre is equal to 100 centimetres. What the statement tells us is
that, for each of the dimensions of our box, we can substitute in 100 centimetres
for each one metre value. That means our height becomes 100
centimetres. Our width becomes 100
centimetres. And our depth becomes 0.02 times
100 centimetres.
So now, let’s write up the volume
of our cube according to these values. That value is equal to 100
centimetres times 100 centimetres times 0.02 times 100 centimetres. Notice that when we multiply all
these terms together, we’ll get a volume in units of cubic centimetres. And when we do that, we find the
same result from earlier, 20000 centimetres cubed. So then, we’ve seen that there are
20000 cubic centimetres in 0.02 cubic metres.
