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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 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 the 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's my water tank and I'm gonna make it transparent so that we can see what's going on inside of the tank so here we go just like a helicopter outside or something I don't know if y'all hear that but let's see so there is my water tank 12 feet high 12 feet high 5 feet long and 9 feet wide 9 foot 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 sitting at the bottom so let's see if I can draw that so let's it's 4 feet wide 4 feet or I guess we could say 4 feet long 7 feet high so 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 something like this as it's sitting in this tank so this is that metal box and I'll just it's 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 gonna fill the whole thing I'm gonna fill the whole thing with water I'm gonna pour water into this thing and the water is gonna start filling up and it's gonna fill up all the volume of the tank except except where the metal box is it's not gonna be able to fill in that volume because the metal box the metal box is solid it's gonna fill up we're gonna fill it slowly fill this thing up around the metal box so what's the volume that's gonna fill up well it's gonna 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 nine foot by five foot times twelve feet that's the volume of the tank tank volume tank volume and from that we want to subtract the metal box volume so minus four foot by eight feet by eight feet 8 feet by 7 feet by 7 feet by 7 feet this is 4 feet wide it is 8 feet what do they see it's 7 feet high 7 feet high it's 4 feet long and it's 8 feet wide 8 feet wide so this right over here is the volume this is the I guess we could call it the metal box volume the box volume and so what's in between or when you take the tank volume subtract out the box volume that's how much the water can actually fill in so I only do 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 it will fill in everything except for where that blue box is so what's to figure out this value 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 2 24 minus to 2048 I do that right I don't 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 300 300 and then 40 minus 25 or is 16 316 and our units are in cubic feet so the volume of the water to tank 316 cubic feet