Independent Practice : Rectangular Prism GRAHAM CRACKERS A manufacturer wants to double the volume of the graham cracker box.
The manufacturer will either double the height or double the width.
GRAHAM
CRACKERS
a. Which option uses less cardboard? Justify your answer.
h 9 in
w 2 in
16 in.
b. What is the volume of the new graham cracker box?

a). Amount of cardboard required will be less when manufacturer doubles the width.

b). Volume of the new cracker box = 216 in³

Step-by-step 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