Three cubes

The body was created by gluing three identical cubes. Its volume is 192 cm3. What is its surface in dm2?

Correct result:

S =  2.24 dm2

Solution:

V=192 cm3 V1=V/3=192/3=64 cm3 a=V13=643=4 cm a2=a/10=4/10=25=0.4 dm S1=a22=0.42=425=0.16 dm2 S=3 6 S14 S1=3 6 0.164 0.16=5625=2.24 dm2V=192 \ \text{cm}_{3} \ \\ V_{1}=V/3=192/3=64 \ \text{cm}^3 \ \\ a=\sqrt[3]{ V_{1}}=\sqrt[3]{ 64 }=4 \ \text{cm} \ \\ a_{2}=a/10=4/10=\dfrac{ 2 }{ 5 }=0.4 \ \text{dm} \ \\ S_{1}=a_{2}^2=0.4^2=\dfrac{ 4 }{ 25 }=0.16 \ \text{dm}^2 \ \\ S=3 \cdot \ 6 \cdot \ S_{1} - 4 \cdot \ S_{1}=3 \cdot \ 6 \cdot \ 0.16 - 4 \cdot \ 0.16=\dfrac{ 56 }{ 25 }=2.24 \ \text{dm}^2



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