M2 – or square meters – is a unit of area that is two-dimensional, and M3 – or cubic meters – is a unit of volume, which is a three-dimensional space. To convert from area to volume, you need an additional measurement. That measurement may be the thickness of a concrete slab, the length of a cylindrical tube or the height of a pyramid. When you have that extra measurement, multiply it by the area of the corresponding two-dimensional shape to get the volume. This strategy works for converting rectangular shapes into boxes, circular shapes into cylinders and triangular shapes into pyramids. When calculating the area of a circle or the volume of a sphere, you only need one measurement – that of the radius – but you use different formulas for area and volume.
Formulas for Area
If you're laying a rectangular concrete slab, you probably know that you find the area of the slab by measuring the length (L) and width (W) and multiplying those two numbers together. The formula for the area of a rectangle is A = LW. A square has four sides of the same length, so it's a special case. Its area is equal to L2.
If the shape is a triangle with base b and height h, the area is 1/2bh. If the slab happens to be circular, you measure the radius (r), which is it the distance from the center to the perimeter, and use the formula A = πr2. Use only measurements in meters if you want to calculate an area in square meters.
Volume of a Rectangular Slab
Suppose you are pouring a concrete slab with a known area, and you want to know how much concrete to buy. For the answer, you must also determine the thickness of the slab. After you do, you can calculate its volume, which is given by its area multiplied by its thickness. The trick to making a correct calculation is to express the thickness of the slab in the same units as the length and width. If you've measured the length and width in meters and the thickness in centimeters or inches, you must convert the thickness measurement to meters before determining volume. An example will clarify this:
A construction company plans to pour a slab that is 15 meters long, 10 meters wide and 10 centimeters thick. The area of the slab is 15 x 10 = 150 square meters (M2). Before calculating volume, note that 10 centimeters = 0.1 meters. Multiply this number by the area of the slab to get 15 cubic meters (M3), which is the volume of the slab and the amount of concrete you need to buy. For a slab that is 4 inches thick, 1 inch = 2.54 centimeters, which equals 10.16 centimeters or 0.102 meters. In this case, you need 15.3 cubic meters of concrete.
Other Volume Calculations
Knowing the area of the cross-section of a cylinder and the cylinder's height (h), you can calculate the cylinder's volume by multiplying them together, V = Ah. If you only know the radius of the circular cross-section, you can still calculate volume using the expression V = πr2h. The volume of a pyramid equals 1/3Ah, where A is the area of the base and h is the height of the pyramid.
A sphere is a special case; you don't need to know the area of its cross-section to find its volume. All you need to know is the radius because the volume of a sphere is given by the formula V = 4/3πr3.
Keep Your Units Straight
When converting from area to volume, it's important to ensure that all measurements are in the same units. If you've calculated the area in square meters (M2), the extra measurement you need to calculate volume must also be in meters. The subsequent answer will be in cubic meters (M3).
About the Author
Chris Deziel holds a Bachelor's degree in physics and a Master's degree in Humanities, He has taught science, math and English at the university level, both in his native Canada and in Japan. He began writing online in 2010, offering information in scientific, cultural and practical topics. His writing covers science, math and home improvement and design, as well as religion and the oriental healing arts.