Q17 of 292 Page 469

Show that the relative error in the volume of a sphere, due to an error in measuring the diameter, is three times the relative error in the diameter.

Let d be the diameter r be the radius and V be the volume of Sphere


Volume of the sphere is given by =


⇒


Let Δd be the error in d and the corresponding error in V be ΔV.


∴


∴


Hence Proved


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