Square Feet And Cubic Feet - Math Central

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Name: Kim Who is asking: student Level: Middle Question: Is there a relationship between square feet and cubic feet? I tried doing some experiments and stuff to see the relationship between square feet and cubic feet, out of curiosity. What I did was take 9 sq. ft. (which equals 1 sq. yd.) exponent 3 = answer and found the square root of the answer and got 27 (27 cubic feet = 1 cubic yd). Can I use this relationship and make conversions between square feet and cubic feet?
Hi Kim, Square feet and Cubic feet are units of measurement for very different concepts. Square feet are units of area and cubic feet are units of volume. Here is an example. Suppose that I want to put a fish pond in my yard. I have to dig a hole, line it with a pool liner and then fill it with water. I am considering a pool which is 4 feet by 4 feet and 4 feet deep. For the liner I need the bottom: 4 feet by 4 feet or 4 4 = 16 square feet each side: 4 feet by 4 feet or 4 4 = 16 square feet There are 4 sides so it total I need 16 + 4 16 = 80 square feet on liner. The volume of the pool is 4 4 4 = 64 cubic feet so I need 64 cubic feet of water. The other option is a pool which is 10 feet long, 5 feet wide and 1 foot deep. For the liner for this design I need the bottom: 10 feet by 5 feet or 10 5 = 50 square feet each long side: 10 feet by 1 foot or 10 1 = 10 square feet each short side: 5 feet by 1 foot or 5 1 = 5 square feet There are two long sides and two short sides and hence I need 50 + 2 10 + 2 5 = 80 square feet of liner. Hence each pool requires a purchase of 80 square feet of liner. The volume of the second design is 10 5 1 = 50 cubic feet. Hence, although the square footage of the liner required for either design is 80 square feet, the cubic feet of water required is quite different. Penny
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