David Weber, Talei Kunkel, Harriet Simand and, Justin Medved Solutions for Chapter: Perimeter, Area and Volume Environmental Impacts, Exercise 16: Practice 3

Complete your own copy of this table, where all shapes are rectangular prisms.

A box of rice in the shape of a rectangular prism has a length of $12 \mathrm{cm}$, a height of $18 \mathrm{cm}$ and a width of $2.5 \mathrm{cm}$. 

Find the volume of the box.

A box of rice in the shape of a rectangular prism has a length of $12 \mathrm{cm}$, a height of $18 \mathrm{cm}$ and a width of $2.5 \mathrm{cm}$. 

The box says that it contains $7$ ounces of rice. If $1$ ounce has an approximate volume of $30 {\mathrm{cm}}^3$, approximately how many cubic centimeters of rice are in the box?

A box of rice in the shape of a rectangular prism has a length of $12 \mathrm{cm}$, a height of $18 \mathrm{cm}$ and a width of $2.5 \mathrm{cm}$. 

Find the volume of empty space in a box filled with $7$ oz of rice. $\left(\text{Take} 1 \mathrm{oz}=30 {\mathrm{cm}}^3\right)$

A box of rice in the shape of a rectangular prism has a length of $12 \mathrm{cm}$, a height of $18 \mathrm{cm}$ and a width of $2.5 \mathrm{cm}$. 

Design a rectangular prism that would be a better fit for the given volume of rice. Given volume of rice is $210 {\mathrm{cm}}^3$.

New designs for products are constantly being created in an effort to find more ecologically friendly packaging and reduce waste of resources. A clever design for packaging toothpaste is a 'tetra pack' which is shaped like a triangular prism. This design not only cuts out the need for an exterior box, but also allows for packs to fit together compactly for more efficient shipping.
A traditional toothpaste box (rectangular prism) measures $3.8 \mathrm{cm}$ by $4.2 \mathrm{cm}$ by $19 \mathrm{cm}$. Draw a diagram of this, complete with dimensions, and calculate the volume.

New designs for products are constantly being created in an effort to find more ecologically friendly packaging and reduce waste of resources. A clever design for packaging toothpaste is a 'tetra pack' which is shaped like a triangular prism. This design not only cuts out the need for an exterior box, but also allows for packs to fit together compactly for more efficient shipping.
The new tetra pack design has a base width of $3.5 \mathrm{cm}$, height of $16.4 \mathrm{cm}$ and depth of $3.5 \mathrm{cm}$. Calculate volume.

New designs for products are constantly being created in an effort to find more ecologically friendly packaging and reduce waste of resources. A clever design for packaging toothpaste is a 'tetra pack' which is shaped like a triangular prism. This design not only cuts out the need for an exterior box, but also allows for packs to fit together compactly for more efficient shipping.
Both of these prisms contain the same amount of toothpaste. Compare the volume of space the packaging of each takes up.
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