Surface of the cube

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

Result

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

Solution:

V1=1 m3 V=a3 a1=V13=13=1 m S1=6⋅ a12=6⋅ 12=6 m2V_{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
V2=0.001 m3 a2=V23=0.0013=110=0.1 m S2=6⋅ a22=6⋅ 0.12=350=0.06 m2V_{2}=0.001 \ \text{m}^3 \ \\ a_{2}=\sqrt[3]{ V_{2}}=\sqrt[3]{ 0.001 }=\dfrac{ 1 }{ 10 }=0.1 \ \text{m} \ \\ S_{2}=6 \cdot \ a_{2}^2=6 \cdot \ 0.1^2=\dfrac{ 3 }{ 50 }=0.06 \ \text{m}^2
V3=8000 mm3  a3=V33=80003=20 mm S3=6⋅ a32=6⋅ 202=2400 mm2V_{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

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