Difference between revisions of "Convert Square Feet to Cubic Feet"
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#*The height, or how tall the space is, is always measured from base to base, at the same point on each. So if you measure from the corner of the floor, you need to go to the same corner in the ceiling. | #*The height, or how tall the space is, is always measured from base to base, at the same point on each. So if you measure from the corner of the floor, you need to go to the same corner in the ceiling. | ||
#*A regular prism is one where the two bases are even and equal polygons, such as triangles, squares, circles, diamonds, etc.<reF>http://www.mathwarehouse.com/solid-geometry/triangular-prism/formula-volume-triangular-prism.php</ref> | #*A regular prism is one where the two bases are even and equal polygons, such as triangles, squares, circles, diamonds, etc.<reF>http://www.mathwarehouse.com/solid-geometry/triangular-prism/formula-volume-triangular-prism.php</ref> | ||
| − | #Multiply the base by the height to get the cubic footage of regular shapes. The easiest way to see this is to think of the volume of a rectangle, found using the basic formula <math>Length * Width * Height</math>. Since square footage is found by multiplying length and width, all you have to do now is account for the height. This same principle applies no matter what the base is -- simply multiply square footage by height.<ref>http://www.phschool.com/atschool/Math_Support/rect_prism_volume.html</ref> | + | #Multiply the base by the height to get the cubic footage of regular shapes. The easiest way to see this is to think of the volume of a rectangle, found using the basic formula <math>Length * Width * Height</math>. Since square footage is found by multiplying length and width, all you have to do now is account for the height. This same principle applies no matter what the base is -- simply multiply square footage by height.<ref name="rf1">http://www.phschool.com/atschool/Math_Support/rect_prism_volume.html</ref> |
#*Square Footage = <math>12ft^2</math>, Height = <math>3ft</math> | #*Square Footage = <math>12ft^2</math>, Height = <math>3ft</math> | ||
#**<math>12ft^2 * 3ft =</math> '''''36'' cubic feet''' | #**<math>12ft^2 * 3ft =</math> '''''36'' cubic feet''' | ||
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#*Surface Area = <math>314.16ft^2</math>, Radius= <math>5ft</math> | #*Surface Area = <math>314.16ft^2</math>, Radius= <math>5ft</math> | ||
#**<math>314.16ft^2 * \frac{5}{3} =</math> '''''523.6'' cubic feet''' | #**<math>314.16ft^2 * \frac{5}{3} =</math> '''''523.6'' cubic feet''' | ||
| − | #*'''Note,''' however, that the formula for the volume of a sphere is simply <math>V= \frac{4}{3}\pi *r^3</math> It is often easier to plug in "r" for this equation than to try and convert from square footage.<ref>http://www.mathopenref.com/spherevolume.html</ref> | + | #*'''Note,''' however, that the formula for the volume of a sphere is simply <math>V= \frac{4}{3}\pi *r^3</math> It is often easier to plug in "r" for this equation than to try and convert from square footage.<ref name="rf2">http://www.mathopenref.com/spherevolume.html</ref> |
#Always express your answer in cubic feet after solving. This is a simple way to keep track of measurements whether you're building a garden or finishing up your homework. To finish you answer, you must denote the type of measurements so that a builder, teacher, or friend knows whether "523.6" refers to inches, yards, feet, miles, etc. Remember: volume is ''always'' cubed. There are three acceptable ways to write the units for cubic feet. | #Always express your answer in cubic feet after solving. This is a simple way to keep track of measurements whether you're building a garden or finishing up your homework. To finish you answer, you must denote the type of measurements so that a builder, teacher, or friend knows whether "523.6" refers to inches, yards, feet, miles, etc. Remember: volume is ''always'' cubed. There are three acceptable ways to write the units for cubic feet. | ||
#*'''<math>523.6ft^3</math>''' | #*'''<math>523.6ft^3</math>''' | ||
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#*<math>\frac{6800ft^3}{12fr} = 566.67ft^2</math> | #*<math>\frac{6800ft^3}{12fr} = 566.67ft^2</math> | ||
#*'''The heater will heat a room with a square footage is <math>566.67ft^2</math> and a height of 12ft. | #*'''The heater will heat a room with a square footage is <math>566.67ft^2</math> and a height of 12ft. | ||
| − | #**This strategy is purely for rectangular or cylindrical volumes. It is much more complex for pyramids and spheres. <ref | + | #**This strategy is purely for rectangular or cylindrical volumes. It is much more complex for pyramids and spheres. <ref name="rf1" /> |
| − | #Remember that this conversion only works for regular prisms and spheres. If your shape curves, bends, twists, or is otherwise irregular, you cannot simply convert from square footage to cubic footage. If the object changes size or thickness as it gains height than the measurement of the base -- your square footage -- will no longer be accurate. These types of problems usually require the [[Use Calculus to Rotate Curves Around an Axis|integral calculus]] to solve.<ref>http://www.mathwords.com/r/regular_prism.htm</ref> | + | #Remember that this conversion only works for regular prisms and spheres. If your shape curves, bends, twists, or is otherwise irregular, you cannot simply convert from square footage to cubic footage. If the object changes size or thickness as it gains height than the measurement of the base -- your square footage -- will no longer be accurate. These types of problems usually require the [[Use Calculus to Rotate Curves Around an Axis|integral calculus]] to solve.<ref name="rf3">http://www.mathwords.com/r/regular_prism.htm</ref> |
#*Imagine buying a heater for a room with a pointed ceiling. Now imagine how much more of the room you'd have to heat if the room was perfectly square, instead of pointed at the top. While the square footage of the floor is important, it isn't the only thing determining the cubic footage. | #*Imagine buying a heater for a room with a pointed ceiling. Now imagine how much more of the room you'd have to heat if the room was perfectly square, instead of pointed at the top. While the square footage of the floor is important, it isn't the only thing determining the cubic footage. | ||
