hey there it's Kaleigh and in this lesson we are going to learn to calculate the
volume of some 3d shapes like cubes and right prisms in this lesson we are going
to concentrate on how much space is inside a solid figure since these shapes
all have depth we can think of them as containers volume is how much space is
inside a container let's look at this square prism to start
notice that this prism is made up of cubes we see that the prism is two cubes
long two cubes tall and two cubes deep so we know that the length the height
and the width of this prism we can count how many cubes this prism is made out of
and we would count one two three four five six seven eight cubes or we can
multiply the length two times the height two times the depth two and we get the
same number of cubes eight now let's take a look at how we calculate units
for volume remember for area since we are
multiplying inches by inches we end up with inches squared since we are
multiplying inches by inches by inches in volume we end up getting inches cubed
another way of saying inches cubed is inches raised to the power of three so
we're finding the volume of a solid figure we start with our base which is
our length and our width and then whatever shape our base makes in this
one it's a rectangle then we would stack that same rectangle on top of each other
so it just keeps going taller and and that is our height but notice that
it's always the base being stacked on top so the same shape or cross-section
on the bottom is being layered on top until we get to the height of our figure
so if we look at this shape here what do we have for our base yeah it's a
rectangle and if we find the area of the base of our prism by our formula area
equals length times width or in this case five inches times 2 inches we will
get 10 square inches now if we know the area of our base we can think about
stacking our base rectangle until we get to a height of 3 inches if we imagine
there are 3 1-inch cubes here we would see that we need to multiply our base by
an area of 3 inches so we will have 10 inches squared times 3 inches and this
gives us a volume of 30 inches cubed and this is how we can determine a formula
for volume we can find the area of the base and multiply it by the height we
can write this formula as V equals B times H where B stands for the area of
the base
now what if we have a triangular prism let's look carefully here what do you
think the base of this prism is remember a prism has two parallel and congruent
bases so if this solid our bases are triangles so we need to find the big B
in our formula and we know how to find the area of triangles so we can use the
formula a is equal to base times height over two and for this triangle that will
give us five inches times six inches over two and that gives us 30 inches
squared over 2 which gives us 15 inches squared so that's the area of our base
here or that big B now what do we do with that big B we have to multiply it
by the height of our prism so looking over at our prism here we see that our
triangle bases are connected by edge lengths of seven inches so that is the
height of our prison prism so we can say the volume is equal to 15 inches squared
times 7 inches which gives us a hundred and five inches cubed and that's our
volume let's do this example together so we need to find the area of our base
first so here we can imagine that there is a rectangular base down here that has
length and width of six inches and three inches so big B is going to be length
times width width of our base which is 6 inches times 3 inches and 6 times 3 that
gives us 18 inches squared so that's my B and now I need to multiply my B times
the height of my prism which I can see is this side length here
which is four inches so if I say B is equal to 18 inches squared times 4
inches that will give me a total volume of 72 inches cubed so the total volume
of my prism here is 72 inches cubed and now you know how to find the volume for
cubes and write prisms great work practice what you've learned by doing
the online games and quizzes have fun and remember to always be clever