Given that 405 cubic centimeters of
water is poured into a rectangular-prism-shaped vessel with a square base whose side
length is nine centimeters, find the height of water in the vessel.
In his question, we’ve been given
some information about the volume of water being poured into a
rectangular-prism-shaped vessel. This vessel has a square base with
side length of nine centimeters. So let’s sketch this out. Here is this vessel. Now, we don’t know what the height
of the water is in the vessel when it’s poured in. So, let’s call that ℎ
centimeters. We do know that the amount of space
this takes up in three dimensions is 405 cubic centimeters. And we also know that this is the
volume. And the volume of a cuboid is equal
to the area of its base multiplied by its perpendicular height.
Now, we can calculate the area of
the base of our vessel. It’s simply a square. So, its area is nine multiplied by
nine, which is 81. We’re working in centimeters. So, the area of the base of our
vessel is 81 square centimeters. We, in fact, also know that the
volume of our water is 405 cubic centimeters. And we’ve said that its height is
equal to ℎ.
We can, therefore, form an equation
in ℎ. We can say that 405, remember,
that’s the volume, is equal to the area of the base, that’s 81, times ℎ or 405
equals 81ℎ. We want to solve for ℎ. So, we’re going to divide both
sides of our equation by 81. That gives us ℎ is equal to
five. And we can, therefore, say that the
height of water in the vessel is five centimeters.