# Write whether Tru

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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