Question

A sphere is inscribed in a cube. Explain the relationship between the surface areas of the two solid figures.

Answer 1

sphere has a radius of "r"

cube has a side of "2r"

SA of sphere is 4 *pi *r^2
Sa of cube is 6* (2r)^2

Answer 2

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.

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

`4\pi r^2`

And Surface area of cube would be

`6a^2\\\\=6(2r)^2\\\\=6* 4r^2\\\\=24r^2`

`\frac{\text{Surface area of cube}}{\text{Surface area of sphere}}=(24r^2)/(4* (22)/(4)r^2)=(24)/(22)=(12)/(11)=1.09=1.1`

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.