Surface of the cube

Find the surface of the cube that has volume
1/1m³
2/0.001 m³
3/8000 mm³

Correct answer:

S₁ =  6 m²
S₂ =  0.06 m²
S₃ =  2400 mm²

Step-by-step explanation:

$$\begin{gathered} V_1=1{\text{m}}^3 \\ V=a^3 \\ {a}_1=\sqrt[3]{V_1}=\sqrt[3]{1}=1\text{ m } \\ {S}_1=6\cdot a_1^2=6\cdot 1^2=6{\text{m}}^2 \end{gathered}$$

$$\begin{gathered} V_2=0.001{\text{m}}^3 \\ {a}_2=\sqrt[3]{V_2}=\sqrt[3]{0.001}={\displaystyle \frac{1}{10}}=0.1\text{ m } \\ {S}_2=6\cdot a_2^2=6\cdot 0.1^2={\displaystyle \frac{3}{50}}={\displaystyle \frac{3}{50}}{\text{m}}^2=0.06{\text{m}}^2 \end{gathered}$$

$$\begin{gathered} V_3=8000{\text{mm}}^3 \\ {a}_3=\sqrt[3]{V_3}=\sqrt[3]{8000}=20\text{ mm } \\ {S}_3=6\cdot a_3^2=6\cdot 20^2=2400{\text{mm}}^2 \end{gathered}$$

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