Cube corners

Peter cut 2 small cubes with edge 5 cm from the corners of a wooden cube with edge 100 cm. How many more small cubes of edge 5 cm can be cut from the remaining wood?

Final Answer:

x =  7998

Step-by-step explanation:

$$\begin{gathered} a=100\text{cm} \\ b=5\text{cm} \\ {V}_1=a^3=100^3=1000000{\text{cm}}^3 \\ {V}_2=b^3=5^3=125{\text{cm}}^3 \\ x=\frac{V_1}{V_2}-2=\frac{1000000}{125}-2=\frac{1000000}{125}-\frac{2\cdot 125}{125}=\frac{1000000}{125}-\frac{250}{125}=\frac{1000000-250}{125}=\frac{999750}{125}=7998 \end{gathered}$$

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