Question

the dimensions of a rectangular block measured with a instrument having least count 0.01cm is 4.0mm*10.0mm*10.0mm.the maximum percentage error in the measurements of volume of the block is​

Answer 1

Dear Student,

◆ Answer -

∆V/V % = 4.5 %

● Explanation -

# Given -

s1 = 4 mm

s2 = 10 mm

s3 = 10 mm

LC = 0.01 cm = 0.1 mm

# Solution -

Here, absolute error in measurement of each side can be least count of instrument. i.e. ∆s = LC.

Volume of the block is given by -

V = s1 × s2 × s3

Differentiating,

∆V/V % = ∆s/s1 % + ∆s/s2 % + ∆s/s3 %

∆V/V % = 0.1/4 × 100 + 0.1/10 × 100 + 0.1/10 × 100

∆V/V % = 2.5 + 1 + 1

∆V/V % = 4.5 %

Therefore, maximum percentage error in the measurements of volume of the block is 4.5 %.

Thanks for asking..