Answer:
4. 256 in²
5. 1163 in²
7. Package A: A = 492 in²; V = 504 in³
Package B: A = 404 in²; V = 528 in³
If two packages have the same volume, the flatter one will have the greater surface area.
Explanation:
Q4.
2 sides = 2(12 in × 5 in) = 2 × 60 in² = 120 in²
Front + back = 2(12 in × 4 in) = 2 × 48 in² = 96 in²
Top + bottom = 2( 5 in × 4 in) = 2 × 20 in² = 40 in²
Total area = 256 in²
Q5. Game box
Top + bottom = 2(15 in × 16 in) = 2 × 240 in² = 480 in²
2 sides = 2(16 in × 11 in) = 2 × 176 in² = 352 in²
Front + back = 2(15 in × 11 in) = 2 × 165 in² = 330 in²
Total area = 1162 in²
Q7. Justify conclusions
Package A
2 sides = 2(14 in × 12 in) = 2 × 168 in² = 336 in²
Top + bottom = 2(14 in × 3 in) = 2 × 42 in² = 84 in²
Front + back = 2(12 in × 3 in) = 2 × 36 in² = 72 in²
Total area = 492 in²
V = lwh = 14 in × 12 in × 3 in = 504 in³
Package B
Top + bottom = 2(11 in × 8 in) = 2 × 88 in² = 176 in²
2 sides = 2(11 in × 6 in) = 2 × 66 in² = 132 in²
Front + back = 2( 8 in × 6 in) = 2 × 48 in² = 96 in²
Total area = 404 in²
V = 11 in × 8 in × 6 in = 528 in³
Package B has about 5 % more volume but 20 % less surface area than Package A.
That's because the area:volume (A:V) ratio decreases the closer the shape is to a sphere.
Package B has A:V = 0.75:1; Package A has A:V = 0.98:1.
The packages have about the same volume, but the flatter package has a greater surface area.