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# 7.E: Dimensional Analysis (Exercises)

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#### Exercise $$\PageIndex{1}$$:

Convert 6 feet 4 inches to centimeters.  Fact:  1 inch = 2.54 cm

#### Exercise $$\PageIndex{2}$$:

Convert 850 square feet to square meters.  Why do you think that Real-estate sites like to list house area regarding square feet instead of square meters?   Fact:  1 foot = 0.3048m

#### Exercise $$\PageIndex{3}$$:

John claims that the surface area of a cone is given by the formula: $$A=\pi r \sqrt{r+h}$$

where $$r$$ is the radius of the cone and $$h$$ is the height of the cone. How can you convince John, he must be wrong without resorting to showing her a formula in a textbook?

#### Exercise $$\PageIndex{4}$$:

Yahoo Autos cites the fuel efficiency of the 2008 Toyota Prius is 4L/100 km in the City and 4.2 L/100 km on the highway.  American site states that Toyota's 2008 Prius hybrid car uses an average 48 miles per gallon in city driving, and 45 mpg on the highway.  Do these figures agree?  According to the Canadian figures, if I spend about \$20 per week in city driving in a 2008 Prius, roughly how many kilometers have I traveled?

#### Exercise $$\PageIndex{5}$$:

At what temperature do Celsius and Fahrenheit agree?

Exercise $$\PageIndex{6}$$:

The exterior dimensions of a freezer are  48 inches by 36 inches by 24 inches, and it is advertised as being 27.0 cubic ft.Is the advertised volume correct?

Exercise $$\PageIndex{7}$$:

Which holds more soup: a can with a diameter of 3 inches and height of 4 inches or a can with the diameter of 4 inches and a height of 3 inches?

Exercise $$\PageIndex{8}$$:

A larger cube has a volume of  81 $$m^3$$. A smaller cube has the length of the edges one-third of the length of the edges of the larger cube. What is the volume of the smaller cube?

Exercise $$\PageIndex{9}$$:

A larger equilateral triangle was created using four smaller equilateral triangles as shown in the figure. The perimeter of the smaller triangle is 18 cm, then what is the perimeter of the larger equilateral triangle?