Ratio 52

The ratio of the surface area of ​​a cube to its volume is 2:1.Calculate:
a) the length of the edge of the cube in cm
b) the volume of the cube in cm³
c) the volume of the cube in cm²

Correct answer:

a =  3 cm
V =  27 cm³
S =  54 cm²

Step-by-step explanation:

$$\begin{gathered} S:V=2:1 \\ S/V=2 \\ S=2V \\ S=6a^2 \\ V=a^3 \\ 6a^2=2\cdot a^3 \\ 6=2\cdot a \\ a=6/2=3\text{cm} \end{gathered}$$

$V=a^3=3^3=27{\text{cm}}^3$

$S=6\cdot a^2=6\cdot 3^2=54{\text{cm}}^2$

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