Question

The dimensions of a rectangular block measured with a vernier calliper having least count 0.1 mm is 5.0 mm × 10.0 mm × 10.0 mm. The maximum percentage error in the measurement of volume of the block is? Answer fast please......needed urgently. ..

Answer 1

The dimensions of a rectangular block measured with a vernier calliper having least count 0.1 mm is 5.0 mm × 10.0 mm × 10.0 mm.

we know, formula of volume , V = lbh

using log both sides,

logV = log(lbh)

or, logV = logl + logb + logh

differentiating both sides,

or, dV/V = dl/l + db/b + dh/h

or, ∆V/V = ∆l/l + ∆b/b + ∆h/h

= 0.1/5 + 0.1/10 + 0.1/10

= 0.02 + 0.01 + 0.01

= 0.04

or, ∆V/V = 0.04

or, ∆V/V × 100 = 0.04 × 100 = 4

or, % error in volume of rectangular box = 4%