Write whether True or False and justify your answer.If a sphere is ins

1.	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.

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.