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Q.

If a sphere is inscribed in a cube, then is it true that the ratio of the volume of the cube to the volume of the sphere will be 6 : p?

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a

True

b

False 

answer is A.

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Detailed Solution

It is given a sphere and a cube.
Let a be the side of the cube and d be the diameter of the sphere.
So, a=d  .
And r be the radius of the sphere so, r= a 2  .
Volume of the cube V=  a 3  .
The volume of the sphere,
V (s) = 4 3 π r 3   V (s) = 4 3 ×π× a 3 8    V (s) = a 3 π 6   Their ratio,
  V V (s) = a 3 : a 3 π 6      V V (s) = 6 π  or  6 p  , where p=π   Hence, the given statement is true.
Correct option is 1.
 
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