A Vernier calipers is used to measure the length, width and the height of the block. The measured values are found to be 1.37 cm, 4.11cm and 2.56 cm respectively. Calculate the volume of the block with the limit of error?

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Answer 1 · 2018-04-22T01:33:00

The volume of the block is #"14.2 cm"^3 ± "0.2 cm"^3#.

The formula for the volume of a rectangular solid is

#color(blue)(bar(ul(|color(white)(a/a)V = lwhcolor(white)(a/a)|)))" "# where

#lcolor(white)(l) ="# the length
#w ="# the width
#h ="# the height

Then, the volume of your block is

#V = "4.11 cm × 2.56 cm × 1.37 cm" = "14.4 cm"^3#

The limit of error

The limit of error is the maximum overestimate and the maximum underestimate from your measurements.

Assume that the uncertainty in your measurements is ±0.01 cm.

If all your measurements were 0.01 cm lower, the volume would be #"14.2 cm"^3#.

If all your measurements were 0.01 cm higher, the volume would be #"14.6 cm"^3#.

Thus, your calculations give a volume between #"14.2 cm"^3# and #"14.6 cm"^3#.

You could report your answer as #"14.2 cm"^3 ± "0.2 cm"^3#, where "14.2" is the result of your measurements and "0.2" is the limit of error.