Cube edge reduction

If we reduce the length of the cube edge by 30%, this cube has a reduced surface area of 1176 cm². Find the edge length and volume of the original cube.

Final Answer:

a =  19.6039 cm
V =  7534.056 cm³

Step-by-step explanation:

$$\begin{gathered} S=6a^2 \\ q=100\%-30\%=1-\frac{30}{100}=0.7 \\ 1176=6a^2-6(q\cdot a{)}^2 \\ 1176=6a^2-6q^3\cdot a^2 \\ 1176=6a^2(1-q^2) \\ a=\sqrt{\frac{1176}{6-6\cdot q^2}}=\sqrt{\frac{1176}{6-6\cdot 0.7^2}}=19.6039\text{cm} \end{gathered}$$

$$\begin{gathered} V=a^3=19.6039^3\doteq 7534.056{\text{cm}}^3 \\ \text{ Verifying Solution: } \\ {S}_1=6\cdot a^2=6\cdot 19.6039^2=\frac{39200}{17}\doteq 2305.8824{\text{cm}}^2 \\ b=q\cdot a=0.7\cdot 19.6039\doteq 13.7227\text{cm} \\ {S}_2=6\cdot b^2=6\cdot 13.7227^2=\frac{19208}{17}\doteq 1129.8824{\text{cm}}^2 \\ x=S_1-S_2=\frac{39200}{17}-\frac{19208}{17}=\frac{39200-19208}{17}=\frac{19992}{17}=1176{\text{cm}}^2 \end{gathered}$$

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