Question

The length and radius of a cylinder are respectively (10+-0.2)cm and (5+-0.3)cm. Calculate the
percentage error in finding its volume​

Answer 1

given, Length of cylinder = (10 ± 0.2) cm.

% error in length = ∆l/l × 100

here ∆l = 0.2 and l = 10

so, % error in length = 0.2/10 × 100 = 2%

radius of base of cylinder = (5 ± 0.3)cm

% error in radius = ∆r/r × 100

here, ∆r = 0.3 and r = 5

so, % error in radius = 0.3/5 × 100 = 6%

we know, volume of cylinder, V = πr²l

so, % error in Volume = 2 × % error in r + 1 × % error in l

= 2 × 6% + 1 × 2%

= 12 % + 2%

= 14%

hence, percentage error in volume = 14%