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l\lore'Ahout Cereal Hoxes
Activity
Cereal Box Sizes
1. The manufacturer of Nutty Crunch wants to know how n
cardboard would be used for the boxes described in Cerel
Sizes, For the sake of simplicity. ignore the cardboard wa!
manufacturing process. Also ignore places where the can
overlaps. In other words. simply find the total surface are
hoxes.
a. Find the surface area of the standard box.
A standard box of Nutty Crunch cereal is 10 inches tall. 8 inches wide.
and 2 inches deep.
1. Find the volume of the box.
2. The manufacturer is thinking about seUing Nutty Crunch in other box sizes.
Find the volume of each of these sizes.
2 inches
--y
8 inches
a. A minisize box that is half as tall.
half as wide, and half as deep as the standard box h. An institutional-size box that is three
times as tall. three times as wide. and three times as deep as the standard box t
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10 inches
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h. Find the surface area of the mini size box.
c. Find the surface area of the institutional-size box.
2. Compare the three surface areas. As in Cereal Box Sizes, (
than simply say which is larger and which is smaller.
./
3. H. Find the surface area of the supersize box. Try to do tl
computing the dimensions of this box.
b. State a general principle for what happens to a box's s
when each dimension is multiplied by the same amou
3. Compare the volumes you found in Question 2 with the volume of
the standard box. Look for more detail than simply. "The minisize is
smaller. The institutional size is larger."
-1. a. Find the volume of a supersize box-five times as tall. five times
as wide. and five times as deep as the standard box. Try to do
this without computing the dimensions of the box. Use your
comparison in Question 3 for ideas.
b. State a general principle for what happens to the volume of a box
when each dimension is multiplied by tbe same amount.
c. Explain your answer to part b. You might want to use
c. Explain your answer to part b. Use diagrams as needed.
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Do Bees Build It Best?: From Two Dimensions to Three
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A Size Summarv .,t
In Cereal Box Sizes and More About Cereal Boxes, you examined
how the volume and surface area of a rectangular solid change if its
dimensions are all multiplied by a specific scale factor.
1. Summarize your conclusions from those two activities.
2. Consider a rectangular solid that is 2 inches by 3 inches by 5 inches.
a. Find the volume and surface area of this solid.
b. Find the volume and surface area of a rectangular solid that is
6 inches by 9 inches by 15 inches using the conclusions you
stated in Question 1. Explair how you used those conclusions.
c. Find the dimensions of a rectangular solid with the same shape
as the original but with a volume of 150 cubic inches. Give the
dimensions to the nearest tenth of an inch.
d. Find the dimensions of a rectangular solid with the same shape
as the original but with a surface area of 124 square inches. Give
the dimensions to the nearest tenth of an inch.
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Do Bees Buiid It Best?: From Two Dimensions to Three
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