The uncertainty in the volume measurement of the spherical beach ball is 0.011%.
The given parameters;
the radius measurement , r = 0.846 ± 0.04 m
first radius = 0.846 m
second radius = 0.04 m
The volume of a sphere is given as;
[tex]V=\frac{4}{3} \pi r^3\\\\[/tex]
The volume of the sphere with the measurement ;
[tex]V=\frac{4}{3} \pi r^3\\\\V_1 = \frac{4}{3} \pi \times (0.846)^3\\\\V_1 = 2.537 \ m^3[/tex]
The volume of the sphere with the absolute uncertainty;
[tex]V=\frac{4}{3} \pi r^3\\\\V_2 = \frac{4}{3} \pi \times (0.04)^3\\\\V_2 = 0.000268 \ m^3[/tex]
The uncertainty in the volume measurement is calculated as;
[tex]\% \ uncertainty = \frac{absolute \ uncertainty }{measurement} \times 100\%\\\\\% \ uncertainty = \frac{0.000268}{2.537} \times 100\%\\\\\% \ uncertainty = 0.011 \ \%[/tex]
Thus, the uncertainty in the volume measurement of the spherical beach ball is 0.011%.
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