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If a rectangular solid have edges, 4 cm, 5 cm and 7 cm, is inscribed in a sphere. How will I get the volume and surface area of the sphere?

Do I need to get the volume of the rectangular solid and use it to get the radius of the sphere?

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  • $\begingroup$ If you visualize, then the diagonal of the cuboid will be a diameter of the sphere. Take out the diagonal of cuboid, and half it to get the radius. $\endgroup$
    – Rohinb97
    Commented Feb 26, 2014 at 13:37
  • $\begingroup$ Then the radius will be 4.74? Am I right? $\endgroup$
    – user114811
    Commented Feb 26, 2014 at 13:59
  • $\begingroup$ @user114811: that is approximately correct. I think it would be better to leave it as $3\sqrt{10}$, which is exact. $\endgroup$ Commented Jun 24, 2015 at 0:01

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You need to use pythagoras twice to find the length of the long diagonal of the cuboid - the long diagonals will be diameters of the sphere.

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