Volume is the amount of space in an object. The fraction occupied by the cube is: [tex]\frac{r\sqrt2}{\pi(r + 2)}[/tex]
First, we calculate the volume of the cube.
[tex]Volume = Length^3[/tex]
From the figure, we have:
[tex]Length = r\sqrt 2[/tex]
So:
[tex]V_1 = (r\sqrt2)^3[/tex]
[tex]V_1 = (2\sqrt2)r^3[/tex]
Next, the volume of the cylinder
[tex]Volume=\pi r^2h[/tex]
So, we have:
[tex]V_2 = \pi r^2 (2r + 4)[/tex]
The fraction (n) occupied by the cube is:
[tex]n = \frac{V_1}{V_2}[/tex]
So, we have:
[tex]n = \frac{(2\sqrt2)r^3}{\pi r^2(2r + 4)}[/tex]
Factor out 2 in the denominator
[tex]n = \frac{(2\sqrt2)r^3}{2\pi r^2(r + 2)}[/tex]
Cancel out common terms
[tex]n = \frac{r\sqrt2}{\pi(r + 2)}[/tex]
Hence, the fraction occupied by the cube is: [tex]\frac{r\sqrt2}{\pi(r + 2)}[/tex]
Read more about volumes at:
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