Question

The radius and length of a cylinder is measured as (2.25+/- 0.02)cm and (6.50+/- 0.01)cm respectively. Find the volume within the error limits and the percentage error in the determination of volume.

Units and Measurements, Physics.
Class XIth.

Answer 1

Answer:

plus them both plz mark it as brain list

Answer 2

EXPLANATION :-

• Radius = (2.25 ± 0.02), where
• r = 2.25 [average value]
• ∆r = 0.02 [mean absolute error]

• Length = (6.50 ± 0.01)
• l = 6.50 [average value]
• ∆l = 0.01 [mean absolute error]

$\sf \rightarrow \: volume \: of \: cylinder = \pi {r}^{2} l$

$\sf \rightarrow \: \frac{\triangle v}{v} = 2 \frac{\triangle r}{r} + \frac{\triangle l}{l}$

$\sf \rightarrow \%v = 2 \frac{\triangle r}{r} \times 100 + \frac{\triangle l}{l} \times 100$

$\sf \rightarrow\%v = 2 \times \frac{0.02}{2.25} \times 100 + \frac{0.01}{6.50} \times 100$

$\sf \rightarrow\%v = \frac{8}{9} + \frac{2}{13}$

$\sf \rightarrow\%v = \frac{104 + 18}{117}$

$\sf \rightarrow\%v = \frac{122}{117} \%$

${ \boxed{\sf \rightarrow\%v =1.04\%}}$