Aussie Maths & Science Teachers: Save your time with SmarterEd
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 |
|
|
|
|
`34`
`text(Consider the cube sliced vertically into 3 equal parts:)`
`text(Cubes with red on at least one side)`
`= 12 + 10 + 12`
`= 34`
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?
`80`
`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` |
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` |
|
|
|
|
|
`24`
`24`