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6. A rectangular plate has a length of (`21.3 +- 0.2`) cm and a width of (`9.8 +- 0.1`) cm. Calculate the area of the plate, including its uncertainty.
6. A rectangular plate has a length of (21.3 +- 0.2) cm and a width of (9.8 +- 0.1) cm. Calculate the area of the plate, including its uncertainty. `(∆A)/A =(∆L)/L + (∆W)/W`
`(209 ± 4) cm^2`
Area:
`A = WL = 21.3 cm times 9.8 cm = 208.74 cm^2 ≈ 209 cm^2`
Uncertainty:
`(∆A)/A =(∆L)/L + (∆W)/W`
`(∆A) =((∆L)/L + (∆W)/W)A`
`∆A = (0.2 / 21.3 + 0.1/9.8) times 208.74 cm^2 = 4.17 cm^2≈ 4 cm^2`
Answer
`(209 ± 4) cm^2`
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