Question

8-1 practice and problem solving: a/b1. the plan of a terrace is shown at right. the scale is 2 inches : 6 feet. what are the length and width of the terrace? find the terraces arealength: _____width: ___area: ___2. the floor plan of a ballroom is shown at right. the scale is 3 centimeters : 4 meters. what are the length and width of the ballroom? find the ballrooms area.length: ___width: ___area: _____3. 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?4. 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?5. 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 1

Step1: Find scale factor

Scale: $2$ in $=6$ ft, so $1$ in $=3$ ft

Step2: Calculate terrace length

Length: $5 \times 3 = 15$ ft

Step3: Calculate terrace width

Width: $2 \times 3 = 6$ ft

Step4: Calculate terrace area

Area: $15 \times 6 = 90$ sq ft

Problem 2

Step1: Find scale factor

Scale: $3$ cm $=4$ m, so $1$ cm $=\frac{4}{3}$ m

Step2: Calculate ballroom length

Length: $12 \times \frac{4}{3} = 16$ m

Step3: Calculate ballroom width

Width: $9 \times \frac{4}{3} = 12$ m

Step4: Calculate ballroom area

Area: $16 \times 12 = 192$ sq m

Problem 3

Step1: Find scale factor

Scale: $1$ unit $=15$ ft, so $1$ ft $=\frac{1}{15}$ unit

Step2: Calculate drawing length

Length: $150 \times \frac{1}{15} = 10$ units

Step3: Calculate drawing width

Width: $120 \times \frac{1}{15} = 8$ units

Problem 4

Part a

Step1: Convert units to match

$4.2$ ft $= 4.2 \times 0.3048 = 1.28016$ m

Step2: Simplify scale ratio

Scale: $1.28016:525 = 1:410.156 \approx 1:410$ (or use feet: $525$ m $=1722.44$ ft, $4.2:1722.44=1:410.1$)

Part b

Step1: Convert model height to inches

$4.2$ ft $= 4.2 \times 12 = 50.4$ inches

Step2: Calculate sheet count

Sheets: $\frac{50.4}{0.6} = 84$

Problem 5

Part a

Step1: Calculate model height

Model height: $20 \times 2.4 = 48$ cm

Step2: Calculate bottle cap count

Caps: $\frac{48}{1.2} = 40$

Part b

Step1: Calculate popsicle stick count

Sticks: $\frac{48}{15.2} \approx 3.16 \approx 3$ (rounded to whole stick)

Answer:

1. Length: 15 ft, Width: 6 ft, Area: 90 sq ft
2. Length: 16 m, Width: 12 m, Area: 192 sq m
3. Length: 10 units, Width: 8 units
4. a. 1:410 (model:actual, in same units)

b. 84 sheets

1. a. 40 bottle caps

b. 3 popsicle sticks