Question

area:

1. a garage floor measures 150 feet by 120 feet. a scale drawing of the floor on grid paper uses a scale of 1 unit : 15 feet. what are the dimensions of the drawing?
2. the scale model of a skyscraper being built is 4.2 feet tall.

a. when it is finished, the skyscraper will be 525 meters tall. what scale was used to make the model?
b. the model is made out of a stack of plywood sheets. each sheet is 0.6 inch thick. how many sheets of plywood tall is the model?
you have been asked to build a scale model of a restaurant out of bottle caps. the restaurant is 20 feet tall. your scale is 2.4 cm : 1 foot.
a. a bottle cap is 1.2 cm tall. about how many bottle caps tall will your model be?
b. you are out of bottle caps and decide to use popsicle sticks instead. you measure them, and they are 15.2 cm tall. how many popsicle sticks tall will your model be?

Explanation:

Problem 3

Step1: Calculate length of drawing

Divide actual length by scale factor.
$\frac{150}{15} = 10$ units

Step2: Calculate width of drawing

Divide actual width by scale factor.
$\frac{120}{15} = 8$ units

Problem 4a

Step1: Convert units to match

Convert 525 meters to feet: $525 \times 3.28084 \approx 1722.44$ feet

Step2: Find scale ratio

Simplify model:actual height.
$\frac{4.2}{1722.44} = \frac{1}{410.1} \approx 1:410$ (or convert model to meters: $4.2 \times 0.3048 \approx 1.28016$ m, $\frac{1.28016}{525} = \frac{1}{410.1} \approx 1:410$)

Problem 4b

Step1: Convert model height to inches

$4.2 \times 12 = 50.4$ inches

Step2: Divide by sheet thickness

$\frac{50.4}{0.6} = 84$ sheets

Problem a (Restaurant Model)

Step1: Calculate model height

Multiply actual height by scale.
$20 \times 2.4 = 48$ cm

Step2: Divide by bottle cap height

$\frac{48}{1.2} = 40$ caps

Problem b (Restaurant Model)

Step1: Use model height from prior step

Model height = 48 cm

Step2: Divide by popsicle stick height

$\frac{48}{15.2} \approx 3.16$, round to 3 sticks

Answer:

1. 10 units by 8 units

4a. 1 unit (model) : 410 units (actual, or 1 foot : 410 feet / 1 meter : 410 meters)
4b. 84 sheets
a. 40 bottle caps
b. Approximately 3 popsicle sticks