BUILDING VOLUME

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BUILDING VOLUME
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DESCRIPTION OF A CUBE

• WHAT IS A CUBE?

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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?

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DESCRIPTION OF A CUBE

• IT HAS 6 FACES.

5
2
4
3
1
6
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DESCRIPTION OF A CUBE

• Two faces intersect in a segment called an edge.
• How many edges does a cube have?

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DESCRIPTION OF A CUBE

• IT HAS 12 EDGES.

width
height
length
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DESCRIPTION OF A CUBE

• Three faces intersect in a point called a vertex.
• How many vertices does a cube have?

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DESCRIPTION OF A CUBE

• IT HAS 8 VERTICES.

6
7
2
3
5
8
1
4
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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.

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BUILDING CUBES
Compare your answer.
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BUILDING CUBES

• Use the snap cubes to build the next larger cube.
• What is the size of the cube?

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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.

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BUILDING CUBES

• How do your answers compare with these?

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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?

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BUILDING CUBES

• Size of the cube is 3x3x3.
• Complete the table for this cube

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BUILDING CUBES

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

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BUILDING CUBES

• Use the snap cubes to build the next larger cube.
• How large is the cube?

ANSWER
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BUILDING CUBES

• Size of cube is 4x4x4.

• Complete the cube table for this cube.

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BUILDING CUBES

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

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BUILDING CUBES

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

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BUILDING CUBES

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

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BUILDING CUBES

• Here is the 5x5x5 cube.

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BUILDING CUBES
Compare your answer.
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BUILDING CUBES

• Use your patterns to complete the table for these
  cubes.
• 6x6x6 7x7x7
• 8x8x8 9x9x9
• 10x10x10

ANSWER
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BUILDING CUBES
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BUILDING CUBES

• 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?

ANSWER
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BUILDING CUBES

• Since n is the measurement of the edge, edge
  length is n- units long.
• What is the perimeter of each face?

ANSWER
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DISCUSSION

• Perimeter 2 length 2 width 2n 2n 4n
• What is the area of each face?

ANSWER
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DISCUSSION

• Area width x length n x n n2.
• What is the surface area?

ANSWER
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DISCUSSION

• A cube has 6 faces. If each face area is n2, then
  surface area is 6n2.
• What is the volume?

ANSWER
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DISCUSSION

• Volume length x width x height.
• Volume n x n x n n3.
• Now use your symbolic representations to complete
  the table for a 15x15x15 cube.

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BUILDING CUBES

• Compare your answer.

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