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Learning Math Home
Measurement Session 9: Solutions
 
Session 9 Part A Part B Part C Homework
 
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measurement Site Map
Session 9 Materials:
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A B C 
Homework

Video

Solutions for Session 9, Part C

See solutions for Problems: C1 | C2 | C3 | C4 | C5


Problem C1

Size of the
Cutout
Square (cm)

Dimensions
of the Box
(cm)

Volume
of the Box
(cm3)

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

<< back to Problem C1


 

Problem C2

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


 

Problem C3

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


 

Problem C4

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


 

Problem C5

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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