building volume the university of texas at dallas

BUILDING VOLUMEBUILDING VOLUME

The University of Texas at Dallas

DESCRIPTION OF A CUBEDESCRIPTION OF A CUBE

WHAT IS A CUBE?WHAT IS A CUBE?



A cube is a three-dimensional geometric A cube is a three-dimensional geometric figure with all sides made of squares figure with all sides made of squares called faces.called faces.

How many faces does a cube have?How many faces does a cube have?



IT HAS 6 FACES.IT HAS 6 FACES.


12

34

5

6


Two faces intersect in a segment called an Two faces intersect in a segment called an edge.edge.

How many edges does a cube have?How many edges does a cube have?



IT HAS 12 EDGES.IT HAS 12 EDGES.


length

height

width


Three faces intersect in a point called a Three faces intersect in a point called a vertex.vertex.

How many vertices does a cube have?How many vertices does a cube have?



IT HAS 8 VERTICES.IT HAS 8 VERTICES.

2

41

58

7

3

6


BUILDING CUBESBUILDING CUBES

Complete the cube table using a single Complete the cube table using a single cube.cube.

Surface area is the sum of the areas of all Surface area is the sum of the areas of all the faces.the faces.

Volume is the number of cubes needed for Volume is the number of cubes needed for the figure – or how many cubes will fit the figure – or how many cubes will fit inside the shape.inside the shape.




Size of Size of CubeCube

Edge Edge LengthLength

(Distance)(Distance)

Perimeter Perimeter of Side of Side (Face)(Face)

Area of Area of SideSide

Surface Surface AreaArea

VolumeVolume

1x1x11x1x1 11 4 units4 units 1 square 1 square unitsunits

6 square 6 square unitsunits

1 cubic 1 cubic unitsunits

Compare your answer.


Use the snap cubes to build the next Use the snap cubes to build the next larger cube.larger cube.

What is the size of the cube?What is the size of the cube?



The size of the cube is 2 x 2 x 2 or 2 units The size of the cube is 2 x 2 x 2 or 2 units length x 2 units width x 2 units height.length x 2 units width x 2 units height.

Complete the cube table for this single Complete the cube table for this single cube.cube.


How do your answers compare with these?How do your answers compare with these?


Size of CubeSize of Cube

Edge LengthEdge Length


Perimeter of Perimeter of Side (Face)Side (Face)

Area of SideArea of Side Surface AreaSurface Area VolumeVolume


24 24 square square unitsunits




Look at your answers for the 1x1x1 cube Look at your answers for the 1x1x1 cube and the 2x2x2 cube. Do you notice any and the 2x2x2 cube. Do you notice any patterns on the table?patterns on the table?

Now build the next larger cube.Now build the next larger cube.

How large is the cube?How large is the cube?


BUILDING CUBESBUILDING CUBES Size of the cube is 3x3x3.Size of the cube is 3x3x3.

Complete the table for this cubeComplete the table for this cube


How do your answers compare with these?How do your answers compare with these? Do your patterns still work?Do your patterns still work?








VolumeVolume






Use the snap cubes to build the next Use the snap cubes to build the next larger cube.larger cube.

How large is the cube?How large is the cube?


ANSWER

Size of cube is 4x4x4.Size of cube is 4x4x4.



Complete the cube table for this cube.Complete the cube table for this cube.

How do your answers compare with these?How do your answers compare with these? Do your patterns still work?Do your patterns still work?








VolumeVolume

4x4x44x4x4 44 16 units16 units 16 16 square square unitsunits




Use your pattern to complete the table for Use your pattern to complete the table for a 5x5x5 cube.a 5x5x5 cube.



Now build the cube to see if your patterns Now build the cube to see if your patterns work.work.





•Here is the 5x5x5 cube.









VolumeVolume




Compare your answer.

Use your patterns to complete the table Use your patterns to complete the table for these cubes.for these cubes.

6x6x66x6x6 7x7x77x7x7 8x8x88x8x8 9x9x99x9x9 10x10x1010x10x10



ANSWER



SizeSize Edge Edge LengthLength

FaceFace Area of 1 Area of 1 FaceFace


VolumeVolume


216 sq 216 sq unitsunits


7x7x77x7x7 77 28 units28 units 49 sq 49 sq unitsunits



8x8x8 8x8x8 88 32 units32 units 64 sq 64 sq unitsunits








1000 1000 cubic cubic unitsunits

Use symbols to explain the patterns you Use symbols to explain the patterns you found.found.

If n is the number of units on the edge of a If n is the number of units on the edge of a cube, what is the edge length?cube, what is the edge length?



ANSWER

Since “n” is the measurement of the edge, Since “n” is the measurement of the edge, edge length is n- units long.edge length is n- units long.

What is the perimeter of each face?What is the perimeter of each face?



ANSWER

Perimeter = 2 length + 2 width = 2n +2n = 4nPerimeter = 2 length + 2 width = 2n +2n = 4n

What is the area of each face?What is the area of each face?

DISCUSSIONDISCUSSION


ANSWER

Area = width x length = n x n = nArea = width x length = n x n = n22..

What is the surface area?What is the surface area?



ANSWER

A cube has 6 faces. If each face area is nA cube has 6 faces. If each face area is n22, then , then surface area is 6nsurface area is 6n22..

What is the volume?What is the volume?



ANSWER

Volume = length x width x height.Volume = length x width x height. Volume = n x n x n = nVolume = n x n x n = n33..

Now use your symbolic representations to Now use your symbolic representations to complete the table for a 15x15x15 cube.complete the table for a 15x15x15 cube.











VolumeVolume



3375 3375 cubic cubic unitsunits

• Compare your answer.

building volume the university of texas at dallas

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