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The measurements obtained for the interior dimensions of a rectangular box are 200 cm by 200 cm by 300 cm. If each of the three measurements has an error of at most 1 cm, which of the following is closest to the maximum possible difference, in cubic cm, between the actual capacity of the box and the capacity computed using these measurements?A. 100,000.B. 120,000.C. 160,000.D. 200,000.E. 320,000.

Respuesta :

Answer:

C. 160,000

Step-by-step explanation:

Given that the measurements obtained for the interior dimensions of a rectangular box are 200 cm by 200 cm by 300 cm.

Also given that each of the three measurements has an error of at most 1 cm

COnsider the worst case where each dimension is increased by 1 cm

Then we measure the dimensions as 201 , 201 and 301

So volume would be measured as

[tex]201*201*301\\= 12160701[/tex] cubic cm

Actual volume of the box = [tex]200*200*300\\=12000000[/tex] cubic cm

Difference maximum possible = 160701 cubic cm

Out of the five options given option C is nearest to this value

So answer is

C. 160,000

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