David Weber, Talei Kunkel, Harriet Simand and, Justin Medved Solutions for Chapter: Perimeter, Area and Volume Environmental Impacts, Exercise 22: Unit review

Tiny houses have become popular in the United State as a way of simplifying life, but also of being more ecologically friendly. With a living 

space of less than $46 m^2$, tiny houses use less materials to build , required less energy and can built on smaller amounts of land . The tiny houses below are two example of deigns from which customers can choose.

The house on the left has interior dimensions of $2.5 m\times 18 m\times 2.8 m$. The triangular house has base dimensions of $4 m\times 10 m$, maximum height of $7 m$ and slant height of $7.3 m$.

Find the amount of space inside each house.

The two centre windows, have parallel measuring $4.5 m$ and $3.5 m$ , respectively . The bottom ( horizontal ) side measures $1.5 m$ . The area of each outer window is equal to that of each centre window. If the parallel sides of the outer windows measures $2.8 m$ and $0.4 m$, what is the length of the bottom side.

The Saskatchewan glacier , in the Columbia ice fields of Alberta, Canada, can be approximated by a rectangular prism with a length of $13 km$, a width of $2.5 km$ and a depth of $1 km$. Find the area of the surface of the glacier that is exposed to air. ( This is everthing except the bottom surface).

The Saskatchewan glacier , in the Columbia ice fields of Alberta, Canada, can be approximated by a rectangular prism with a length of $13 km$, a width of $2.5 km$ and a depth of $1 km$. Find the volume of ice in the glacier.

The Saskatchewan glacier , in the Columbia ice fields of Alberta, Canada, can be approximated by a rectangular prism with a length of $13 km$, a width of $2.5 km$ and a depth of $1 km$. If the length , width and depth are all cut in half, how would the volume of ice compare to the current amount? State the percentage decrease that this would represent.

Each of these compost bins has a square base , measuring $1 m$ by $1 m$. The front panel is $1.2 m$ high and the back panel is $1.5 m$ high.

Calculate the volume of compost the set of three compost bins could hold when filled to capacity.

Show that a rectangular prism with dimensions $4\times 6\times 12$ has a surface area that is numerically equal to its volume.

There are nine other rectangular prisms with whole number sides that have a surface area numerically equal to their volume, one of the cube . Find the dimensions of the cube and one of the other rectangular prisms.