smc-672-60-Number of faces/edges

Geometry, NAP-E4-NC21

A T-shaped prism is pictured below.

How many edges does the prism have?

`10`	`19`	`20`	`22`	`24`

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`24`

Show Worked Solution

`text(Edges on T face) = 8`

`text(Edges connecting top and bottom) = 8`

`:.\ text(Total edges)`	`= 2 xx 8 + 8`
	`= 24`

Craig has a drum which has the top and bottom in the shape of regular octagons, as shown below.

The other faces are isosceles triangles.

How many edges does Craig's drum have?

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`32`

Show Worked Solution

`text(Top and bottom edges)`

`= 8 xx 2 = 16`

`text(Side edges)`

`= 8 xx 2 = 16`

`:.\ text(Total edges )`	`= 16 + 16`
	`= 32`

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`