Formulas for Lengths, Areas and Volumes

One-dimensional Measurement Let’s consider the following formulas for calculating the lengths of figures. Perimeter of a rectangle = 2(a + b) The lengths in the figures are sums of the lengths (or multiples of the lengths) of some line segments. We say that the measurement of length is a linear measurement, i.e. one-dimensional measurement.

Two-dimensional Measurement Let’s consider the following formulas for calculating the areas of figures. Area of a square = a2 Area of a parallelogram = ah Total surface area of a cuboid = 2(ab + bc + ac)

The areas of the figures are the products of two lengths (or sum of the products of two lengths). We say that the measurement of area is a quadratic measurement, i.e. two-dimensional measurement.

Three-dimensional Measurement Let’s consider the following formulas for calculating the volumes of solids. h r 2 3 1 p Volume of a circular cone = 3 4 r p Volume of a sphere = The volumes of the solids are the products of three lengths (or sum of the products of three lengths). We say that the measurement of volume is a cubic measurement, i.e. three-dimensional measurement.

Let’s try to determine the dimensions of the following measurements.  It includes the product of two lengths (i.e. r 2). r Dimension = _________ 2 (b)  It includes the product of three lengths (i.e. r 2h). Dimension = _________ 3

(c) 4(a + b + c) Dimension = _________ 1 (d) Dimension = _________ 2  It includes the sum of lengths. Dimension = _________ 1 (d) l  It includes the product of two lengths (i.e. rl ). Dimension = _________ 2