1. BUILDING VOLUME The University of Texas at Dallas

2. DESCRIPTION OF A CUBE  WHAT IS A CUBE? The University of Texas at Dallas

3. DESCRIPTION OF A CUBE  A cube is a three-dimensional geometric figure with all sides made of squares called faces.  How many faces does a cube have? The University of Texas at Dallas

4. DESCRIPTION OF A CUBE  IT HAS 6 FACES. The University of Texas at Dallas 1 2 3 4 5 6

5. DESCRIPTION OF A CUBE  Two faces intersect in a segment called an edge.  How many edges does a cube have? The University of Texas at Dallas

6. DESCRIPTION OF A CUBE  IT HAS 12 EDGES. The University of Texas at Dallas length height width

7. DESCRIPTION OF A CUBE  Three faces intersect in a point called a vertex.  How many vertices does a cube have? The University of Texas at Dallas

8. DESCRIPTION OF A CUBE  IT HAS 8 VERTICES. 2 4 1 5 8 7 3 6 The University of Texas at Dallas

9. BUILDING CUBES  Complete the cube table using a single cube.  Surface area is the sum of the areas of all the faces.  Volume is the number of cubes needed for the figure – or how many cubes will fit inside the shape. The University of Texas at Dallas

10. BUILDING CUBES The University of Texas at Dallas Size of Cube Edge Length (Distance) Perimeter of Side (Face) Area of Side Surface Area Volume1x1x1 1 4 units 1 square units 6 square units 1 cubic units Compare your answer.

11. BUILDING CUBES  Use the snap cubes to build the next larger cube.  What is the size of the cube? The University of Texas at Dallas

12. BUILDING CUBES  The size of the cube is 2 x 2 x 2 or 2 units length x 2 units width x 2 units height.  Complete the cube table for this single cube. The University of Texas at Dallas

13.  How do your answers compare with these? BUILDING CUBES Size of Cube Edge Length (Distance) Perimeter of Side (Face) Area of Side Surface Area Volume2x2x2 2 8 units 4 square units 24 square units 8 cubic units The University of Texas at Dallas

14. BUILDING CUBES  Look at your answers for the 1x1x1 cube and the 2x2x2 cube. Do you notice any patterns on the table?  Now build the next larger cube.  How large is the cube? The University of Texas at Dallas

15. BUILDING CUBES  Size of the cube is 3x3x3.  Complete the table for this cube The University of Texas at Dallas

16.  How do your answers compare with these?  Do your patterns still work? BUILDING CUBES Size of Cube Edge Length (Distance) Perimeter of Side (Face) Area of Side Surface Area Volume3x3x33 12 units 9 square units 54 square units 27 cubic units The University of Texas at Dallas

17. BUILDING CUBES  Use the snap cubes to build the next larger cube.  How large is the cube? The University of Texas at Dallas ANSWER

18.  Size of cube is 4x4x4. BUILDING CUBES The University of Texas at Dallas  Complete the cube table for this cube.

19.  How do your answers compare with these?  Do your patterns still work? BUILDING CUBES Size of Cube Edge Length (Distance) Perimeter of Side (Face) Area of Side Surface Area Volume4x4x44 16 units 16 square units 96 square units 64 cubic units The University of Texas at Dallas

20.  Use your pattern to complete the table for a 5x5x5 cube. BUILDING CUBES The University of Texas at Dallas

21.  Now build the cube to see if your patterns work. BUILDING CUBES The University of Texas at Dallas

22. BUILDING CUBES The University of Texas at Dallas Here is the 5x5x5 cube.

23. BUILDING CUBES The University of Texas at Dallas Size of Cube Edge Length (Distance) Perimeter of Side (Face) Area of Side Surface Area Volume5x5x5 5 20 units 25 square units 25 square units 150 square units 150 square units 125 cubic units Compare your answer.

24.  Use your patterns to complete the table for these cubes. 6x6x67x7x7 6x6x67x7x7 8x8x89x9x9 8x8x89x9x9 10x10x10 10x10x10 BUILDING CUBES The University of Texas at Dallas ANSWER

25. BUILDING CUBES The University of Texas at DallasSize Edge Length Face Area of 1 Face Surface Area Volume6x6x66 24 units 36 square units 216 sq units 216 cubic units 7x7x77 28 units 49 sq units 294 sq units 343 cubic units 8x8x88 32 units 64 sq units 384 sq units 512 cubic units 9x9x99 36 units 81 sq units 484 sq units 729 cubic units 10x10x1010 40 units 100 sq units 600 sq units 1000 cubic units

26.  Use symbols to explain the patterns you found.  If n is the number of units on the edge of a cube, what is the edge length? BUILDING CUBES The University of Texas at Dallas ANSWER

27.  Since “n” is the measurement of the edge, edge length is n- units long.  What is the perimeter of each face? BUILDING CUBES The University of Texas at Dallas ANSWER

28.  Perimeter = 2 length + 2 width = 2n +2n = 4n  What is the area of each face? DISCUSSION The University of Texas at Dallas ANSWER

29.  Area = width x length = n x n = n 2.  What is the surface area? DISCUSSION The University of Texas at Dallas ANSWER

30.  A cube has 6 faces. If each face area is n 2, then surface area is 6n 2.  What is the volume? DISCUSSION The University of Texas at Dallas ANSWER

31.  Volume = length x width x height.  Volume = n x n x n = n 3.  Now use your symbolic representations to complete the table for a 15x15x15 cube. DISCUSSION The University of Texas at Dallas

32. BUILDING CUBES The University of Texas at Dallas Size of Cube Edge Length (Distance) Perimeter of Side (Face) Area of Side Surface Area Volume15x15x15 1 5 1 5 60 units 225 square units 225 square units 1350 square units 1350 square units 3375 cubic units Compare your answer.