Question

Find the ratio of the volume of a cube to that of a sphere which will fit inside it.

Answer 1

Let the radius of the shere be R and the edge of the cube be a.

As the sphere is fit inside the cube .

so, diameter of the sphere =edge of the cube 

⇒ 2R = a               ...........(i)

Now,

The ratio of the cube to that of the sphere`= "Volume of the cube"/"Volume of the sphere"`

`=a^3/((4/3pi"R"^3))`

`=(2"R")^3/((3/4pi"R"^3))`               [Using  (i)]

`=(3xx8"R"^3)/(4pi"R"^3)`

`=6/pi`

`=6 : pi`

so,the ratio of the Volume of the cube to that of the sphere is 6 : π.