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} = 8r^{3} …(i)

Volume of the sphere is given by,

Volume of the sphere = 4/3 π(radius)^{3}

= 4/3 πr^{3} …(ii)

Using equations (i) & (ii),

Volume of the cube : Volume of the sphere = 8r^{3} : 4/3 πr^{3}

= 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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