Cube surface area

The surface of the cube was originally 216 centimeters square. The surface of the cube has shrunk from 216 to 54 centimeters sq. Calculate how much percent the edge of the cube has decreased.

Result

p =  50 %

Solution:

S1=216 cm2 S2=54 cm2 a1=S1/6=216/6=6 cm a2=S2/6=54/6=3 cm p=(a1a2)/a1 100=(63)/6 100=50=50%S_{1}=216 \ \text{cm}^2 \ \\ S_{2}=54 \ \text{cm}^2 \ \\ a_{1}=\sqrt{ S_{1}/6 }=\sqrt{ 216/6 }=6 \ \text{cm} \ \\ a_{2}=\sqrt{ S_{2}/6 }=\sqrt{ 54/6 }=3 \ \text{cm} \ \\ p=(a_{1}-a_{2})/a_{1} \cdot \ 100=(6-3)/6 \cdot \ 100=50=50 \%



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