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Distance, Area, and Volume

When we measure distances we use measurements of length: cm, metres, yards, miles. Conceptually we use a measuring stick and step off how many units it takes to cover the length of the object. In the example below we will use feet.

When we measure areas we imagine a square tile, 1 foot by 1 foot, and see how many of those tiles it would take to cover the area. We call that measurement a square foot. If you imagine a rectangular space like your bedroom you can do the calculation. If the bedroom is 12 feet long and 9 feet wide, it will take 9*12 = 108 tiles of 1 square foot to cover it. So its area is 108 square feet. Notice that it takes 2 units of length to define an area, whereas only 1 was needed for a length.

In 3D we measure volumes, using the same concept that we did for areas except that we use a cubic foot instead of a square foot. Yes, you guessed it. a cubic foot is like a big sugar cube, i foot long, 1 foot wide, and 1 foot high. Because volumes measure 3D objects, we count how many of the i foot-on-a-side cubes would fill it. For example, suppose you have to fill a container truck that is 30 feet long, 6 feet wide, and 8 feet high. How many cubic feet will it take? 30*6 will cover the floor but they will only be 1 foot high! To fill the container you need 8 layers, so the total is 30*6*8 = 1,440 cubic feet.

How big is a square mile, in square yards ( 1 mile = 1,760 yards)? Because it is measured in square miles, we know that it represents an area and that the units we are going to use are square yards. If we lay out our 1 square yard tiles, it will take 1,760 of them to stretch 1 mile, and it will only be 1 yard wide. To cover the square mile, you will need 1,760 rows of them, so 1,760*1,760 = 3,097,600.

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