Answer:
a). Amount of cardboard required will be less when manufacturer doubles the width.
b). Volume of the new cracker box = 216 in³
Explanation:
Volume of the Graham cracker box = volume of the rectangular prism formed
= Length × Width × Height
= 6 × 2 × 9
= 108 in³
a). To double the volume of the rectangular prism, manufacturer either doubles the height or doubles the width.
When manufacturer doubles the height,
Amount of cardboard required = surface area of the rectangular prism
= 2(lw + wh + hl)
= 2(6×2 + 2×18 + 18×6)
= 2(12 + 36 + 108)
= 2(66)
= 132 in²
When manufacturer doubles the width,
Surface area of the rectangular prism = 2(6×4 + 4×9 + 9×6)
= 2(24 + 36 + 54)
= 2(114)
= 228 in²
Therefore, amount of cardboard required will be less when manufacturer doubles the width.
b). Volume of the new Graham box = 2(Volume of the old box)
= 2 × 108
= 216 in³