I have a hollow sphere and would like to determine its volume. I decide to measu

Question

I have a hollow sphere and would like to determine its volume. I decide to measure its circumference by wrapping a string around its "equator", and using a meter stick I measure the length of that circumference-string to be 0.82 m ± 0.01 m. Recalling that the circumference of a circle of radius r is 2*pi*r and the volume of a sphere is , (4/3)*pi r^3 please calculate with five digits to the right of the decimal point the volume of my sphere and the absolute uncertainty (same as absolute error) in that volume.

Explanation / Answer

          circumference = C = 2 R = 0.82 m ± 0.01   m            thus, uncertainity in radious = R = C / 2   = (0.82 ± 0.01 )/2(3.14)                                                                                  = (0.13 ± 0.00159 )                            volume of the sphere =V = 4/3 R3                              uncertianity in the volume = V = 4 R2 R                                                                       = 4(3.14)(0.13)2(0.00159)                                                                        =  0.00033749976            

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