Converting Volumes, Such As Cubic Inches To Cubic FeetDate: 02/09/2004 at 13:12:51 From: Cindy Subject: Buying correct amount of sand to fill sandbox. First of all, I'm not a student, just a stumped adult. I would like to fill a sandbox with 3 inches of sand. The sandbox measures 25ft X 80ft. How much sand do I need to buy? I've tried using the volume formula by converting feet to inches, and then checking my answer by converting inches to feet. I get two different answers, so I'm doing something wrong. Here's what I have: 25 ft = 300 inches L 80 ft = 960 inches W 3 inches D Total volume is 300*960*3 = 864,000 cubic inches or 72,000 cubic feet or 24,000 cubic yards. Now, using feet - 25ft = 25ft 80ft = 80ft 3in = .25ft Total volume is 25*80*.25 = 500 cubic feet or 166.6 cubic yards. What am I doing wrong here? Date: 02/09/2004 at 18:27:18 From: Doctor Jeremiah Subject: Re: Buying correct amount of sand to fill sandbox. Hi Cindy, The total volume is indeed 864000 cubic inches. It's your conversion back to cubic feet that doesn't work, and there's a good reason why. Imagine a cube 12 inches x 12 inches x 12 inches. That cube is only 1 cubic foot in size, but its volume is 12x12x12 = 1728 cubic inches. To convert 864000 cubic inches to cubic feet you must divide by 12x12x12. And 864000/1728 = 500 cubic feet. A cube that is 3 feet x 3 feet x 3 feet is only 1 cubic yard so to convert 500 cubic feet to cubic yards you must divide by 3x3x3. And 500/27 = 18.5 cubic yards. Here is another way to look at it: 25ft 80ft .25ft (25 x 80 x .25) cubic ft --------- x --------- x --------- = ----------------------------- 3 ft/yard 3 ft/yard 3 ft/yard (3 x 3 x 3) cubic ft/cubic yd Now it's a little more obvious why you need to divide by 3x3x3 when you are converting cubic feet to cubic yards. And the same thing could be done for cubic inches to cubic feet like this: 300in 960in 3in (300 x 960 x 3) cubic in -------- x -------- x -------- = ----------------------------- 12 in/ft 12 in/ft 12 in/ft (12 x 12 x 12) cubic in/cubic ft Let me know if you have more questions about this. - Doctor Jeremiah, The Math Forum http://mathforum.org/dr.math/ Date: 02/09/2004 at 21:48:33 From: Cindy Subject: Thank you (Buying correct amount of sand to fill sandbox.) Thank you so very much for your wonderful response! I appreciate your assistance! |
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