Answer: The relationship between the surface areas of the two solid figures is that the surface area of cube is 1.1 times the surface of cube.
Step-by-step explanation:
Since we have given that
A sphere is inscribed in a cube.
Let the radius of sphere be 'r'.
Let the side of cube would be the diameter of sphere i.e. 2r.
So, Surface area of sphere would be
[tex]4\pi r^2[/tex]
And Surface area of cube would be
[tex]6a^2\\\\=6(2r)^2\\\\=6\times 4r^2\\\\=24r^2[/tex]
[tex]\dfrac{\text{Surface area of cube}}{\text{Surface area of sphere}}=\dfrac{24r^2}{4\times \dfrac{22}{4}r^2}=\dfrac{24}{22}=\dfrac{12}{11}=1.09=1.1[/tex]
So, the relationship between the surface areas of the two solid figures is that the surface area of cube is 1.1 times the surface of cube.
