Q. 94.0( 3 Votes )

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.

Answer :

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.


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