 # 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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You are given that the volume of the cube-shaped hideaway is 8 ft^{3}.The volume of a cube is ${s}^{3}$ where ss is the side length so ${s}^{3}=8$. Cube rooting both sides gives $s=3\sqrt{8}=2$ so the side lengths of the cube are s=2 ft.
The surface area of a cube is $6{s}^{2}$ 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 $6{\left(2\right)}^{2}=6\left(4\right)=24f{t}^{2}.$
If each opening has a length and width of 1 ft, then each opening has an area of $1×1=1f{t}^{2}$. Since there are 3 openings, then the total area of the openings is $3×1=33×1=3f{t}^{2}.$
The surface area of the cube that is not openings is then $24f{t}^{2}-3f{t}^{2}=21.$
The fraction of the surface area that is not an opening is then:
surface area that is not openings/total surface area$=\frac{21f{t}^{2}}{24f{t}^{2}}=\frac{7}{8}$