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## Volume of a rectangular prism

Current time:0:00Total duration:4:40

## Video transcript

A water tank is 12 feet high,
5 feet long, and 9 feet wide. A solid metal box which is
7 feet high, 4 feet long, and 8 feet wide is sitting
at the bottom of the tank. The tank is filled with water. What is the volume of
the water in the tank? So let's think about this. We have a water tank. It's 12 feet high. I'll try to draw this
as good as I can. So it's 12 feet high. It's 5 feet long. So this looks like
that's about 5 feet. And it's 9 feet wide. So this is my best rendition
of what a tank looks like. So the tank might look
something like this. That is my water tank. Let me draw it, draw
the whole thing. So there is my water tank. And I'm going to make
it transparent so that we can see what's
going on inside of the tank. So here we go. There's like a helicopter
outside or something, I don't know if
you all hear that. But let's see. So there is my water tank
12 feet high, 5 feet long, and 9 feet wide. And then they say
there's a solid metal box which is 7 feet high, 4
feet long, and 8 feet wide sitting at the bottom. So let's see if I can draw that. So let's say it's 4 feet wide. Or I guess they say 4
feet long, 7 feet high. So let's see, 4 feet might
look something like this. It's 7 feet high, which might
look something like that. 7 feet high. Obviously, I'm not drawing
it perfectly to scale. 7 feet high and 8 feet wide. So it might look
something like this as it's sitting in this tank. So this is that metal box. And they say it's
a solid metal box. It's not like any
water can fit in here. So let me make it as
a solid metal box. So this is a solid metal box. And then I'm going to fill
the whole thing with water. I'm going to pour
water into this thing. And the water's going
to start filling up. And it's going to fill up
all the volume of the tank except where the metal box is. It's not going to be able
to fill in that volume because the metal box is solid. So it's going to fill up. We're going to fill it,
slowly fill this thing up around the metal box. So what's the volume that
it's going to fill up? Well, it's going to
fill up the volume of the tank minus the
volume of the metal box. It couldn't fill in
the metal box volume. So let's figure
out what that is. The volume of the
tank is going to be 9 foot by 5 foot times 12 feet. That's the volume of the tank. Tank volume. And from that, we want to
subtract the metal box volume. So minus 4 foot by
8 feet by 7 feet. This is 4 feet wide. It is 8 feet-- they
say it's 7 feet high. It's 4 feet long. And it's 8 feet wide. So this right over
here is the volume. I guess we could call
it the metal box volume. When you take the tank volume
and subtract out the box volume, that's how much the
water can actually fill in. So I only drew the
water partially filled. But once it's already
filled in, the water is going to go all the
way to the top here. And we'll fill in
everything except for where that blue box is. So let's figure out
what this value is. So 5 times 12 is 60. 60 times 9 is 540. And then in blue
here, let's see. 4 times 8 is 32. 32 times 7 is 210. Plus 14, which is 224. So it's minus 224. Minus 224. Did I do that right? I don't want to make
a careless mistake? So 32 times 7. 2 times 7 is 14. 3, which is really a 30 here. 30 times 7 is 210. Plus another 10 is 220. So 224. So this is going to be
equal to-- let's see. 500 minus 200 is 300. And then 40 minus 24 is 16. 316. And our units are in cubic feet. So the volume of the
water in the tank? 316 cubic feet.