Cube 1-2-3

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

Final Answer:

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

Step-by-step explanation:

$$\begin{gathered} a_1=4 \\ {V}_1=a_1^3=4^3=64{\text{cm}}^3 \end{gathered}$$

$S_1=6\cdot a_1^2=6\cdot 4^2=96{\text{cm}}^2$

$$\begin{gathered} a_2=22/4=\frac{11}{2}=5.5 \\ {V}_2=a_2^3=5.5^3=166.375{\text{cm}}^3 \end{gathered}$$

$S_2=6\cdot a_2^2=6\cdot 5.5^2=181.5{\text{cm}}^2$

$$\begin{gathered} a_3=30/12=\frac{5}{2}=2.5 \\ {V}_3=a_3^3=2.5^3=15.625{\text{cm}}^3 \end{gathered}$$

$S_3=6\cdot a_3^2=6\cdot 2.5^2=37.5{\text{cm}}^2$

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