The diameter of a sphere is measured using a screw gauge having a pitch of 1 mm and 100 divisions on its circular scale. If the measured diameter is 2.50 mm , the maximum percentage error in the calculated volume of the sphere will be:

Step-by-step solution

Least count of the screw gauge = Pitch Number of divisions = 1 mm 100 = 0.01 mm . This least count represents the absolute error in the measurement of the diameter, so d = 0.01 mm . The volume of a sphere is given by V = 4 3 ( d 2 )^3 . The maximum percentage error in volume is: V V 100 = 3 ( d d ) 100 = 3 ( 0.01 2.50 ) 100 = 3 0.4 % = 1.2 % . Answer: 1.2 %