A cuboid has volume V = l l l , where l is the length of one side. When the length l is measured by a meter scale of least count 1 , mm , the relative percentage error in the measurement of its volume is 6.25 % . Then the relative percentage error in measurement of its length and the value of the length l is

Step-by-step solution

Given V = l l l = l^ 5/2 The relative percentage error in volume is given by: V V 100 = 5 2 ( l l 100 ) Substituting the given percentage error in volume: 6.25 = 5 2 ( l l 100 ) l l 100 = 6.25 2 5 = 2.5 % The relative percentage error in the measurement of length is 2.5 % . The least count of the meter scale is l = 1 mm = 0.1 cm . Using the percentage error in length: 0.1 l 100 = 2.5 10 l = 2.5 l = 10 2.5 = 4 cm Answer: 2.5 % and 4 cm