Volume of cubes and rectangular prisms

Learning Objectives Calculate the distance between two points in a three-dimensional coordinate system. Determine the edge lengths of a cube or rectangular prism given the coordinates of its vertices. Identify if a prism defined by coordinates is a cube by comparing its edge lengths. Apply the correct formula to calculate the volume of a rectangular prism (V = lwh). Apply the correct formula to calculate the volume of a cube (V = s³). Solve multi-step problems involving the volume of prisms defined within a 3D coordinate plane. How can the GPS coordinates of a shipping container's corners tell us exactly how much it can hold? 📦 In this lesson, you will bridge the gap between 2D coordinate geometry and 3D shapes. We will use coordinates to define cubes and rectangular...

TermDefinitionExample Rectangular PrismA three-dimensional solid shape which has six faces that are rectangles. It has three dimensions: length (l), width (w), and height (h).A shoebox with vertices at (0,0,0), (5,0,0), (0,3,0), and (0,0,2) defining its corner. CubeA special type of rectangular prism where all six faces are squares and all edges have the same length (s).A die where the length, width, and height are all 2 cm. 3D Coordinate SystemA system used to locate points in three-dimensional space using an ordered triple of numbers (x, y, z), representing distances along the x-axis, y-axis, and z-axis.The point P(3, 4, 5) is located 3 units along the x-axis, 4 units along the y-axis, and 5 units along the z-axis from the origin (0,0,0). Vertex (plural: Vertices)A point where two or mo...

Distance Formula in 3D d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} Use this formula to calculate the length of a line segment (like an edge of a prism) between two points (vertices) P1(x1, y1, z1) and P2(x2, y2, z2) in a 3D coordinate system. Volume of a Rectangular Prism V = l \times w \times h Once you have determined the lengths of the three unique, perpendicular edges (length, width, and height) from the vertices, multiply them together to find the volume. Volume of a Cube V = s^3 If all edge lengths are equal (s), the prism is a cube. Calculate the volume by cubing the side length. This is a special case of the rectangular prism formula where l = w = h = s.