Write whether True or False and justify your answer
If a sphere is inscribed in a cube, then the ratio of the volume of the cube to the volume of the sphere will be 6 : π.
If a sphere is inscribed in a cube, then length of the edge of the cube is equal to diameter of sphere.
So, let length of the edge of the cube = 2r
Then, diameter of the sphere = 2r
⇒ radius of the sphere = 2r/2 = r
Volume of the cube is given by,
Volume of the cube = (length of the edge)3
= (2r)3 = 8r3 …(i)
Volume of the sphere is given by,
Volume of the sphere = 4/3 π(radius)3
= 4/3 πr3 …(ii)
Using equations (i) & (ii),
Volume of the cube : Volume of the sphere = 8r3 : 4/3 πr3
= 8 : 4/3 π
= 2 : 1/3 π
Taking L.C.M (1,3) = 3. Multiply 3 by numerator of each term,
Volume of the cube : Volume of the sphere = 6 : 3/3 π
= 6 : π
Hence, it is true.