# untitled.pdf - Opgave 1 a Vi skal kende rumfanget af...

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Opgave 1 a) Vi skal kende rumfanget af lokalet og af en bordtennisbold. En formel for antallet 𝑛𝑛 kan så være 𝑉𝑉 rum = 𝑛𝑛 ∙ 𝑉𝑉 bold . Vi bestemmer estimater for de to rumfang. 𝑉𝑉 bold = 4 3 𝜋𝜋𝑟𝑟 3 med 𝑟𝑟 = 2 cm får vi 𝑉𝑉 bold = 33.5 cm 3 . Rummets rumfang er 𝑉𝑉 rum = ℎ ∙ 𝑏𝑏 ∙ 𝑑𝑑 , der afhænger af rummet højde, bredde og dybde. Vi sætter = 2.5 m, 𝑏𝑏 = 3 m og 𝑑𝑑 = 4 m. 𝑉𝑉 bold = 30 m 3 . Antallet af bordtennisbolde, 𝑛𝑛 = ℎ∙𝑏𝑏∙𝑑𝑑 4 3 𝜋𝜋𝑟𝑟 3 , findes nu til 𝑛𝑛 = 900000; husk at være opmærksom på at længdeenhederne er forskellige. Der kan altså være omkring én million bordtennisbolde i lokalet. Bemærk at bordtennisbolde ikke kan pakkes så meget som terninger så man kunne justere til et effektivt volumen, men da størrelsen af bolden i forvejen er et estimat gør det ikke den store forskel, det vigtige i estimering er oftest størrelsesordenen.
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