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Solutions for Session 9, Part C
See solutions for Problems: C1 | C2 | C3 | C4 | C5
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Problem C1 | |
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Size of the
Cutout
Square (cm) |
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Dimensions
of the Box
(cm) |
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Volume
of the Box
(cm3) |
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1 by 1 |
1 by 18 by 18 |
324 |
2 by 2 |
2 by 16 by 16 |
512 |
3 by 3 |
3 by 14 by 14 |
588 |
4 by 4 |
4 by 12 by 12 |
576 |
5 by 5 |
5 by 10 by 10 |
500 |
6 by 6 |
6 by 8 by 8 |
384 |
7 by 7 |
7 by 6 by 6 |
252 |
8 by 8 |
8 by 4 by 4 |
128 |
9 by 9 |
9 by 2 by 2 |
36 |
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<< back to Problem C1
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Problem C2 | |
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The largest volume seems to result from a 3-by-3 cutout square (588 cm3). The 4-by-4 square gave nearly as high a volume.
<< back to Problem C2
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Problem C3 | |
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You found that the largest tank would result if you removed 3-by-3 cm squares. The dimensions of the model would be 17 by 17 by 3 cm. Increasing back to the original scale, the dimensions of the tank would be 170 by 170 by 30 cm.
<< back to Problem C3
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Problem C4 | |
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From observing the graph, it becomes evident that the largest value for volume will be between values 3 and 4 on the x-axis.
<< back to Problem C4
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Problem C5 | |
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Using 3.5 as a square's side would give us the volume of 591.5 cm3. Using 3.4 as a square's side, we'd get the volume of 592.4 cm3. The largest volume is achieved when the square is cut with side length 3 1/3 (or 3.333...) cm, leaving 13 1/3 (or 13.333...) cm in the center. The volume is (3 1/3) • (13 1/3) • (13 1/3) = (10/3) • (40/3) • (40/3) = 16,000/27 cm3, or about 592.59 cm3.
<< back to Problem C5
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