Question

lesson 8-1
similar shapes and scale drawings
practice and problem solving: a/b

1. 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 area.

length ____________
width ____________
area ____________

1. 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 ____________

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?

____________

1. 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?
____________

1. 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:

Step1: Convert scale to unit ratio

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

Step2: Calculate terrace length

$5 \text{ in} \times 3 \frac{\text{ft}}{\text{in}} = 15$ ft

Step3: Calculate terrace width

$2 \text{ in} \times 3 \frac{\text{ft}}{\text{in}} = 6$ ft

Step4: Calculate terrace area

$15 \text{ ft} \times 6 \text{ ft} = 90$ ft²

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Step1: Convert scale to unit ratio

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

Step2: Calculate ballroom length

$12 \text{ cm} \times \frac{4}{3} \frac{\text{m}}{\text{cm}} = 16$ m

Step3: Calculate ballroom width

$9 \text{ cm} \times \frac{4}{3} \frac{\text{m}}{\text{cm}} = 12$ m

Step4: Calculate ballroom area

$16 \text{ m} \times 12 \text{ m} = 192$ m²

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Step1: Convert scale to unit ratio

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

Step2: Calculate drawing length

$150 \text{ ft} \times \frac{1}{15} \frac{\text{unit}}{\text{ft}} = 10$ units

Step3: Calculate drawing width

$120 \text{ ft} \times \frac{1}{15} \frac{\text{unit}}{\text{ft}} = 8$ units

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Part a

Step1: Convert units to match

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

Step2: Find scale ratio

$\frac{1.28016 \text{ m}}{525 \text{ m}} = \frac{1}{410.16} \approx \frac{1}{410}$
Scale: $1$ ft $: \frac{525}{4.2}$ m = $1$ ft $: 125$ m

Part b

Step1: Convert model height to inches

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

Step2: Calculate plywood sheets

$\frac{50.4 \text{ in}}{0.6 \frac{\text{in}}{\text{sheet}}} = 84$ sheets

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Part a

Step1: Calculate model height

$20 \text{ ft} \times 2.4 \frac{\text{cm}}{\text{ft}} = 48$ cm

Step2: Calculate bottle caps

$\frac{48 \text{ cm}}{1.2 \frac{\text{cm}}{\text{cap}}} = 40$ caps

Part b

Step1: Calculate popsicle sticks

$\frac{48 \text{ cm}}{15.2 \frac{\text{cm}}{\text{stick}}} \approx 3.16 \approx 3$ sticks

Answer:

1. Length: 15 ft, Width: 6 ft, Area: 90 ft²
2. Length: 16 m, Width: 12 m, Area: 192 m²
3. 10 units by 8 units
4. a. 1 foot : 125 meters, b. 84 sheets
5. a. 40 bottle caps, b. 3 popsicle sticks