Surface 45911

A large cube with an edge of length 3 is given. One small cube with a volume 27 times smaller than the volume of the large cube is glued to each of its faces. All the small cubes touch the big ones through the wall. What surface does this body have?

Correct answer:

S =  78

Step-by-step explanation:

$$\begin{gathered} a=3 \\ V=a^3=3^3=27 \\ {V}_2=V/27=27/27=1 \\ b=\sqrt[3]{V_2}=\sqrt[3]{1}=1 \\ {S}_1=6\cdot a^2=6\cdot 3^2=54 \\ {S}_2=(6-2)\cdot b^2=(6-2)\cdot 1^2=4 \\ S=S_1+6\cdot S_2=54+6\cdot 4=78 \end{gathered}$$

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