Cube 1-2-3

Calculate the volume and surface area of the cube ABCDEFGH if:
a) /AB/ = 4 cm
b) perimeter of wall ABCD is 22 cm
c) the sum of the lengths of all edges of the cube is 30 cm.

Result

V1 =  64 cm3
S1 =  96 cm2
V2 =  166.375 cm3
S2 =  181.5 cm2
V3 =  15.625 cm3
S3 =  37.5 cm2

Solution:

a1=4 V1=a13=43=64 cm3a_{1}=4 \ \\ V_{1}=a_{1}^3=4^3=64 \ \text{cm}^3
S1=6 a12=6 42=96 cm2S_{1}=6 \cdot \ a_{1}^2=6 \cdot \ 4^2=96 \ \text{cm}^2
a2=22/4=112=5.5 V2=a23=5.53=13318=166.375 cm3a_{2}=22/4=\dfrac{ 11 }{ 2 }=5.5 \ \\ V_{2}=a_{2}^3=5.5^3=\dfrac{ 1331 }{ 8 }=166.375 \ \text{cm}^3
S2=6 a22=6 5.52=3632=181.5 cm2S_{2}=6 \cdot \ a_{2}^2=6 \cdot \ 5.5^2=\dfrac{ 363 }{ 2 }=181.5 \ \text{cm}^2
a3=30/12=52=2.5 V3=a33=2.53=1258=15.625 cm3a_{3}=30/12=\dfrac{ 5 }{ 2 }=2.5 \ \\ V_{3}=a_{3}^3=2.5^3=\dfrac{ 125 }{ 8 }=15.625 \ \text{cm}^3
S3=6 a32=6 2.52=752=37.5 cm2S_{3}=6 \cdot \ a_{3}^2=6 \cdot \ 2.5^2=\dfrac{ 75 }{ 2 }=37.5 \ \text{cm}^2



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