Determine: 10182

The lengths of the edges of two cubes are in the ratio 1:2, determine:
a) the ratio of the content of the wall of the smaller cube to the content of the wall of the larger cube.
b) the ratio of the surface of the smaller cube to the surface of the larger cube.
c) the ratio of the volume of the smaller cube to the volume of the larger cube.
Thank you very much

Correct answer:

p₁ =  1:4
p₂ =  1:4
p₃ =  1:8

Step-by-step explanation:

$$\begin{gathered} a:b=1:2 \\ {S}_1=a^2 \\ {S}_2=b^2 \\ {V}_1=a^3 \\ {V}_2=b^3 \\ 2a=b \\ {p}_1=S_1:S_2=a^2:b^2=a^2:(2a{)}^2 \\ {p}_1=1/2^2=0.25=1:4 \end{gathered}$$

$$\begin{gathered} p_2=6S_1:6S_2 \\ {p}_2=S_1:S_2 \\ {p}_2=p_1 \\ {p}_2=1/4=0.25=1:4 \end{gathered}$$

$$\begin{gathered} p_3=V_1:V_2=a^3:b^3 \\ {p}_3=a^3:(2a{)}^3 \\ {p}_3=1/2^3=0.125=1:8 \end{gathered}$$

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