Original 63984

If we reduce the length of the cube edge by 30%, this reduced cube has an area of ​​1176 cm². Specify the edge length and volume of the original cube.

Correct answer:

a =  20 cm
V =  8000 cm³

Step-by-step explanation:

$$\begin{gathered} S=6a^2 \\ q=100\%-30\%=1-\frac{30}{100}=0.7 \\ 1176=6b^2 \\ b=\sqrt{\frac{1176}{6}}=14\text{cm} \\ b=q\cdot a \\ a=b/q=14/\frac{7}{10}=14:\frac{7}{10}=14\cdot \frac{10}{7}=\frac{14\cdot 10}{7}=\frac{140}{7}=20\text{cm} \end{gathered}$$

$$\begin{gathered} V=a^3=20^3=8000=8000{\text{cm}}^3 \\ \text{ Verifying Solution: } \\ {S}_1=6\cdot a^2=6\cdot 20^2=2400{\text{cm}}^2 \\ {S}_2=6\cdot b^2=6\cdot 14^2=1176{\text{cm}}^2 \end{gathered}$$

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