Video Transcript
Find an expression for the volume
of the rectangular prism shown.
And then, we have a rectangular
prism or a cuboid where we’ve been given the three dimensions. Let’s call this dimension here the
length, which I’ve abbreviated to 𝑙. We’ll call this dimension here 𝑤
for width, and then we’ll say this dimension is the height ℎ. And then, we know, of course, that
the volume of a rectangular prism is just the product of these three dimensions. It’s length times width times
height, meaning that the volume of our rectangular prism in cubic units will be
three 𝑥 times 10𝑥 times 15𝑥. And so, we’re actually finding the
product of three monomials. And we recall that to do this, we
first multiply the coefficients; those are the numerical parts. So, we’re going to begin by doing
three times 10 times 15. And then, we separately multiply
the variables. So here, we’re going to do 𝑥 times
𝑥 times 𝑥.
We do also know that multiplication
is commutative, so it can be done in any order. So, we’ll begin by multiplying the
three by the 15 to get 45. And then 45 multiplied by this 10
here is 450. And so, when we multiply the
coefficients of our monomials, we get 450. And now, we multiply the algebraic
parts. 𝑥 times 𝑥 times 𝑥 is 𝑥
cubed. And so, we can say that the volume
of the rectangular prism shown in cubic units is 450𝑥 cubed.
