Video Transcript
A small cube of iron has sides with
length 0.15 meters. If the mass of the cube is 26.6
kilograms, what is its density? Give your answer to three
significant figures.
Okay, so in this example, we have a
cube made of iron. And the sides are all the same
length, 0.15 meters. Along with this, we’re told the
mass of the cube — we can refer to it as 𝑚. And that’s given as 26.6
kilograms. Based on this, we want to calculate
the cube’s density. To do that, let’s recall the
mathematical relationship between density, mass, and volume. The density 𝜌 of a given object is
equal to its mass divided by its volume. So in our case, the density of our
cube, we can call it 𝜌 sub c, is equal to the cube’s mass, 26.6 kilograms, divided
by its volume.
To solve for its volume, we can
recall that since we are working with a cube, the volume of our cube is equal to its
side length cubed. In our case, that side length is
0.15 meters. Therefore, our volume is 0.15
meters quantity cubed. Those parentheses are important
because they tell us that we’ll apply this cube both to the unit of meters as well
as to the number, 0.15. So the volume of our cube is 0.15
cubed cubic meters. When we calculate this density, we
find it’s equal to 7881.48 and so on and so forth kilograms per cubic meter.
But our statement tells us to give
our answer to three significant figures. So let’s start at the front of our
answer and count off three. Here’s one significant figure,
there’s two, and there’s the third one. Now to figure out whether this
second eight here, our third significant figure, will round up or stay the same,
we’ll look at the next digit in our answer. That digit is a one, which is less
than five. So this eight will not round up to
a nine. It will stay as it is. To three significant figures then,
our density is 7880 kilograms per cubic meter. That’s the density of this iron
cube.
