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Geometry, NAP-A4-NC17

Ruby made this solid object using 36 cubes.

   

She then painted the complete surface area of the object red.

The object is then broken apart into 36 cubes.

How many cubes have at least one side painted red?

27 32 34 36
 
 
 
 
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`34`

Show Worked Solution

`text(Consider the cube sliced vertically into 3 equal parts:)`

`text(Cubes with red on at least one side)`

`= 12 + 10 + 12`

`= 34`

Filed Under: 2D-3D Shapes, 2D-3D Shapes Tagged With: Band 8, smc-3185-20-Building blocks, smc-672-20-Building blocks

Geometry, NAP-B4-NC09

Grant joined the two objects below.

Which object below could not be made using Grant's 2 objects?

 
 
 
 
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Show Worked Solution

Filed Under: 2D-3D Shapes, 2D-3D Shapes Tagged With: Band 7, smc-3185-20-Building blocks, smc-672-20-Building blocks

Geometry, NAP-F4-NC09

The shape below was cut into identical pieces and nothing was left over.
 

 

 
Which of the following could be the shape of the pieces?

 
 
 
 
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Show Worked Solution

`text(The larger shape can be cut up as follows:)`

Filed Under: 2D-3D Shapes, 2D-3D Shapes Tagged With: Band 7, smc-3185-10-Identify 2D-3D shapes, smc-3185-20-Building blocks, smc-672-10-Identify 2D-3D shapes, smc-672-20-Building blocks

Geometry, NAP-G4-NC28 SA

The edges of a  4 × 4 × 4  cube are formed using blocks as shown below:
 

 

 
In total, 32 blocks are used.

How many blocks would be needed to make the edges of an  8 × 8 × 8  cube in the same way?

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`80`

Show Worked Solution

`text(Cubes in the top level = 28)`

`text(Cubes in the bottom level = 28)`

`text{Cubes in the vertical pillars (not including top/bottom level)}`

`=4 xx 6`

`= 24`

 

`:.\ text(Total blocks)` `= 28 + 28 + 24`
  `=80`

Filed Under: 2D-3D Shapes, 2D-3D Shapes, 2D-3D Shapes Tagged With: Band 10, smc-3155-60-Number of faces/edges, smc-3185-20-Building blocks, smc-3185-60-Number of faces/edges, smc-672-20-Building blocks, smc-672-60-Number of faces/edges

Geometry, NAP-F4-CA05

9 cubes are used to make an obstacle, pictured below, that is part of a children's adventure playground.
 

 
Gary paints all sides of the step except for the bottom side which sits on the ground.

How many cube faces will Gary paint?

`15` `18` `24` `30` `36`
 
 
 
 
 
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`24`

Show Worked Solution

`24`

Filed Under: 2D-3D Shapes, 2D-3D Shapes Tagged With: Band 6, smc-3185-20-Building blocks, smc-672-20-Building blocks

Geometry, NAP-H4-CA01

Peter made this 3D object using 36 small cubes.
 

 naplan-2015-1mc

 
Which of these has a volume half that of Peter's object?

naplan-2015-1mciii naplan-2015-1mcii naplan-2015-1mci naplan-2015-1mciv
 
 
 
 
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naplan-2015-1mci

Show Worked Solution

`text(The shape with 18 cubes is:)`

naplan-2015-1mci

Filed Under: 2D-3D Shapes, 2D-3D Shapes Tagged With: Band 5, smc-3185-20-Building blocks, smc-672-20-Building blocks

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