The volume of the block after cutting out the smaller cubes is  [tex]\frac{63}{125}[/tex] cubic units.
Given that, Sarah has a solid wooden cube with a length of 4/5 centimetres. From each of its 8 corners, she cuts out a smaller cube with a length of 1/5 centimetre.
We need to find the volume of the block after cutting out the smaller cubes.
The volume of a cube is defined as the total space enclosed by the cube in a three-dimensional space. The formula to find the volume of a cube is a³, where a=edge of a cube.
Now, the volume of a solid wooden cube with a length of 4/5 centimetre
[tex]=(\frac{4}{5} )^{3} =\frac{4}{5} \times \frac{4}{5}\times \frac{4}{5}=\frac{64}{125}[/tex] cubic units.
The volume of a smaller cube with a length of 1/5 centimetre
[tex]=(\frac{1}{5} )^{3} =\frac{1}{5} \times \frac{1}{5}\times \frac{1}{5}=\frac{1}{125}[/tex] cubic units.
The volume of the block after cutting out the smaller cubes[tex]=\frac{64}{125}-\frac{1}{125}=\frac{63}{125}[/tex]
Therefore, the volume of the block after cutting out the smaller cubes is  [tex]\frac{63}{125}[/tex] cubic units.
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