Question

Can anyone help me with this?

Answer 1

==> The man in the lab says that each of his 3 measurements could have been anywhere between 0.05cm too small and 0.05cm too big.

So he's saying that the BIGGEST the volume of the sample could possibly be is if ALL of his measurements are 0.05cm too small. Then the real volume would be

(2.18 cm) x (2.80 cm) x (2.64 cm) = 16.11456 cm³

and the SMALLEST the volume of the sample could possibly be is if ALL of his measurements are 0.05cm too BIG. Then the real volume would be

(2.08 cm) x (2.70 cm) x (2.54 cm) = 14.26464 cm³

==> The lady in the lab says that her final result could have been anywhere between 0.9cm³ too small and 0.9cm³ too big.

So the real volume is somewhere between 15.1cm³ and 16.9cm³ .

The two researchers calculated different volumes, but because of the possible error in each measurement, their range of total volumes overlap.

So the way I see it, the man and the lady researchers overlap each other, but I'm instinctively inclined to suspect that when all is said and done, the lady's measurements are almost certainly more compelling.

Answer 2

Yes, they calculated different volumes but because of the error on each measurement, their range of volumes overlaps with each other.

The error on each measurement of length, width and height has error
`\pm 0.05 \text{cm}`. Recall the volume of a cuboid

`V=lwh = 2.13 \text{cm} * 2.75 \text{cm} * 2.59 \text{cm} = 15.171 \text{cm}^3`.

Next, because we multiplied the terms, we must add the errors.

`\text{Total error for volume} = 0.05\text{cm} + 0.05\text{cm} + 0.05\text{cm} = 0.15\text{cm}^3` (I realise the units don't match up here, I'm not sure why.)

This means the first scientist measured the volume as
`15.171 \pm 0.15 \text{cm}^3`. The second scientist measured the volume as
`16.0 \pm 0.9\text{cm}^3`. We therefore see the range of volumes overlaps and so we say they measured the same volume.