SmarterEd

Aussie Maths & Science Teachers: Save your time with SmarterEd

v1 Measurement, STD2 M1 2023 HSC 9 MC

The length and width of a rectangular pool are measured to be 13 m and 7.5 m respectively, correct to the nearest metre and nearest 0.1 metre.

What are the lower and upper bounds for the area of the pool?

  1. `text{94.25 m}^2\ text{and 101.25 m}^2`
  2. `text{93.125 m}^2\ text{and 101.925 m}^2`
  3. `text{92.5 m}^2\ text{and 102.5 m}^2`
  4. `text{93.75 m}^2\ text{and 100.75 m}^2`
Show Answers Only

`B`

Show Worked Solution
♦ Mean mark 35%.

`text{Length absolute error} = 1/2 xx 1 = 0.5\ \text{m}`

`text{Width absolute error} = 1/2 xx 0.1 = 0.05\ \text{m}`

`text{Length bounds: } 13 ± 0.5 = [12.5,\ 13.5]\ \text{m}`

`text{Width bounds: } 7.5 ± 0.05 = [7.45,\ 7.55]\ \text{m}`

`text{Lower bound area} = 12.5 xx 7.45 = 93.125\ \text{m}^2`

`text{Upper bound area} = 13.5 xx 7.55 = 101.925\ \text{m}^2`

`⇒ B`