Teaching Models

Solid Figures, Surface Area, and Volume

Solid Figures
At this grade level, only right rectangular prisms and cubes are considered.

The surface area of a solid figure is the sum of the areas of all faces of the figure. A net is a two-dimensional pattern that can be cut and folded to make a solid figure. Students use nets to find the areas of the faces of figures. The volume of a solid figure is a measure of the amount of space the figure occupies. The volume of a prism is the area of the base times the height. If the height is 1, then each square unit in the base will give rise to 1 cubic unit of volume in the prism. In general, each unit square in the base corresponds to a rectangular prism with base area 1 and height h. Taking the sum of the volumes results in the formula V = B × h where B is the area of the base and h is the height of the prism. Since the area of the base of a rectangular prism is equal to the length times the width, the formula for the volume of a rectangular prism can also be written as V = l × w × h.

Teaching Model 17.1: Solid Figures

Houghton Mifflin Math Grade 5