Formulas are used to calculate the capacity of an object. It is important in geometry, algebra and calculus to be able to determine the capacity of an object. Different shapes, whether 2D or 3D, use a specific formula based on the shape's dimensions to calculate its capacity.
Volume formulas are used to find the capacity of 3D objects--for example, if you want to find out how much water a can will hold. Cones, spheres, cylinders, prisms and rectangle solids are common shapes for which volume can be calculated. The formula for cones is "1/3 pr2 h." Note that "h" stands for height. For spheres, "4/3 pr3" is used to calculate the volume. The formula for cylinders is "pr2 h." The formula for prisms is "base X height." The formula for rectangular solids is "length X width X height." The volume of a box with a length, width and height of 3 feet is 27 feet cubed. The resulting amount is always cubed, just as the unit is always squared for area problems.
Area formulas are used to find the capacity of two-dimensional objects--for example, squares, rectangles, triangles, trapezoids and circles. For rectangles and squares, the formula used to find the area is "length X width." For triangles, "1/2 (base X height)" will find the area. For trapezoids, the area equals the average of the two bases X height. For example, a trapezoid with a base of 2 and 4 and a height of 6 would have an area of 18 units squared. The formula to find the area of a circle is "pr2," in which "r" stands for radius. For example, if there is a circle with a radius of 5, then the area is 25p.