What, roughly, is the percent uncertainty in the volume of a spherical beach ball of radius ?
The correct answer of percent uncertainty is 10%.
Volume is defined as the amount of space that a particular object or body occupies in the space.
The radius of the spherical beach ball, .
The formula of the volume of a sphere is
From equation (i), the volume is
Thus, the final value of the multiplication is 0.6%.
Differentiating equation (i) w.r.t to radius,
The formula of the small change in the volume of a sphere is
role="math" localid="1643623569468" .
From equation (ii), the small change in the volume is
The formula of percent uncertainty is
From equation (iii), the value of percent uncertainty is
Thus, the final value is 10%.
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