a cube-shaped cat hideaway is 8ft cubed. On 3 sides there is a 1 ft opening. What is the area in fractions of the surface area that is not an opening?

rocedwrp 2020-11-23 Answered
a cube-shaped cat hideaway is 8ft cubed. On 3 sides there is a 1 ft opening. What is the area in fractions of the surface area that is not an opening?
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Expert Answer

Margot Mill
Answered 2020-11-24 Author has 106 answers

You are given that the volume of the cube-shaped hideaway is 8 ft^{3}.The volume of a cube is s3 where ss is the side length so s3=8. Cube rooting both sides gives s=38=2 so the side lengths of the cube are s=2 ft.
The surface area of a cube is 6s2 where ss is the side length. Since the side length is s=2 ft, then the total surface area of the cube including the openings is 6(2)2=6(4)=24ft2.
If each opening has a length and width of 1 ft, then each opening has an area of 1×1=1ft2. Since there are 3 openings, then the total area of the openings is 3×1=33×1=3ft2.
The surface area of the cube that is not openings is then 24ft23ft2=21.
The fraction of the surface area that is not an opening is then:
surface area that is not openings/total surface area=21ft224ft2=78

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