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Current time:0:00Total duration:6:22

Volume of a rectangular prism: word problem

CCSS.Math:

Video transcript

mario has a fish tank that is a right rectangular prism with base 15.6 centimeters by seven point two centimeters so let's try to imagine that so it's a right rectangular prism this is a fish tank let me actually do it in blue so it one of the dimensions that's not blue that's orange one of the dimensions is 15 15 point six centimeters 15 point six centimeters and then the other dimension of the base is seven point two seven seven point two centimeters seven point two centimeters so this is the base right over here so let me draw this try to put some perspective in there and of course it is a right rectangular prism this fish tank that mario has so it looks something like this so this is his fish tank try to draw it as neatly as I can so it's the top of the fish tank just like that I think this does a decent respectable job of what this fish tank might look like and let me erase this thing right over here and there we go there is Mario's fish tank there is a fish tank and we can even make it look like glass there you go that looks nice all right the bottom of the tank is filled with marbles and the tank is then filled with water to a height of six point four centimeters so the water is filled to a height of six point four centimeters so this is the water when it's all filled up six point four centimeters so let's draw that and I'll make the water well maybe I should have made it a little more blue than this but this gives you the picture so the height of the water right over here actually let me do that in a blue color the height of the water right over here is six point four six point four centimeters so that means that the distance from the bottom of the tank to the top of not the tank but to the top of the water is six point four centimeters six point four centimeters there now so that's the top of the water when the marbles were moving it started off with some marbles in on the bottom they don't tell us how many marbles when the marbles are removed the water level drops to a height of five point nine centimeters so when they're removed the water level drops by a little bit to five point nine centimeters five point nine centimeters so it drops it drops to five point it drops to five point nine from six point four to five point nine centimeters what is the volume of the water displaced by the marbles so when you took the marbles out the water dropped from six point four so dropped from six point four centimeters centimeters down to five point nine centimeters five point nine centimeters so how much did it drop well it dropped 0.5 centimeters so dropped it dropped 0.5 centimeters so what does that tell us about the volume of water displaced by the marbles well the volume of water displaced by the marbles must be the amount of that must be equivalent to this volume this volume of this I guess this I guess this is another rectangular prism that is the same where the top area is the same as the base of this water tank and then the height is the height of the water drop when you put the marbles in it takes up more volume it pushes the water up by that amount by that volume when you take it out then that what that volume gets replaced with the water down here and then that volume goes back down the water level goes down to five point nine centimeters so essentially trying to find the volume of a rectangular prism that is that is equal to so it's going to be fifteen point six by seven point two five point five and I haven't drawn it to scale yet but I want to see all of the measurements so it's going to be fifteen point six centimeters in this direction it's going to be seven point two centimeters in this direction it's going to be 0.5 centimeters high 0.5 centimeters high so we know how to find volume we just multiply the length times the width times the height so the volume in centimeter cubed and once again we're multiplying centimeters times centimeters times centimeters so it's going to be centimeters cubed is going to be let me write this down the volume is going to be fifteen point six times seven point two times zero point five it's going to be in centimeters cubed cubic centimeters I guess we could call them well let's first multiply seven point two times zero point five we can do that in our head this part right over here is going to be three point six essentially just half of seven point two so then this becomes fifteen point six times three point six so let me just multiply that over here so fifteen point six times three point six so I'll ignore the decimals for a second 6 times 6 is 36 5 times 6 is 30 plus 3 is 33 1 times 6 is 6 plus 3 is 9 and then let's place a zero here we're down on the ones place but I'm ignoring the decimals for now 3 times 6 is 18 3 times 5 is 15 plus 1 is 16 3 times 1 is 3 plus 1 is 4 and then we get 6 3 plus 8 is 11 16 5 now if this was 156 times 36 this would be 5 thousand six hundred and 16 but it's not we have two numbers to the right of the decimal point one two so it's going to be 56 point one six so the volume the volume let me deserve a drum roll now is 56 point one six cubic cubic centimeters