Integer cube

The length of the cube edge is an integer. Its volume is in cm³, a five-digit number divisible by 1331. What is the length of the edge of this cube?

Correct answer:

a₁ =  22 cm
a₂ =  33 cm
a₃ =  44 cm

Step-by-step explanation:

$$\begin{gathered} 1331=11\times 11\times 11=11^3 \\ V=a^3=(k\cdot 11{)}^3 \\ 9999c{m}^3<V<100000c{m}^3 \\ {V}_1=(1\cdot 11{)}^3=1331{\text{cm}}^3 \\ {V}_2=(2\cdot 11{)}^3=10648{\text{cm}}^3 \\ {V}_3=(3\cdot 11{)}^3=35937{\text{cm}}^3 \\ {V}_4=(4\cdot 11{)}^3=85184{\text{cm}}^3 \\ {V}_5=(5\cdot 11{)}^3=166375{\text{cm}}^3 \\ {a}_1=2\cdot 11=22\text{cm} \end{gathered}$$

$a_2=3\cdot 11=33\text{cm}$

$a_3=4\cdot 11=44\text{cm}$

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