Question

find the missing dimension. use the scale factor 1 : 12.

item	model	actual
corvette	length: in.	length: 15 ft
water tower	depth: 32 cm	depth: m
wingspan	width: 5.4 ft	width: yd
football helmet	diameter: mm	diameter: 21 cm

1. error analysis a scale is 1 cm : 20 m. describe and correct the error in finding the actual distance that corresponds to 5 centimeters.

\\(\frac{1\text{ cm}}{20\text{ m}} = \frac{x\text{ m}}{5\text{ cm}}\\)
\\(x = 0.25\text{ m}\\)

Explanation:

Step1: Define scale factor relation

The scale factor is $\frac{\text{Model}}{\text{Actual}} = \frac{1}{12}$, so $\text{Actual} = 12 \times \text{Model}$ and $\text{Model} = \frac{\text{Actual}}{12}$. Unit conversions are done first where needed.

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Problem 12: Mattress Length

Step1: Calculate actual length

$\text{Actual Length} = 12 \times 6.25$
$\text{Actual Length} = 75$ in.

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Problem 13: Corvette Model Length

Step1: Convert actual length to inches

$15\ \text{ft} = 15 \times 12 = 180\ \text{in.}$

Step2: Calculate model length

$\text{Model Length} = \frac{180}{12}$
$\text{Model Length} = 15$ in.

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Problem 14: Water Tower Actual Depth

Step1: Calculate actual depth in cm

$\text{Actual Depth} = 12 \times 32 = 384\ \text{cm}$

Step2: Convert cm to meters

$\text{Actual Depth} = \frac{384}{100} = 3.84$ m

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Problem 15: Wingspan Actual Width

Step1: Calculate actual width in ft

$\text{Actual Width} = 12 \times 5.4 = 64.8\ \text{ft}$

Step2: Convert ft to yards

$\text{Actual Width} = \frac{64.8}{3} = 21.6$ yd

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Problem 16: Football Helmet Model Diameter

Step1: Convert actual diameter to mm

$21\ \text{cm} = 21 \times 10 = 210\ \text{mm}$

Step2: Calculate model diameter

$\text{Model Diameter} = \frac{210}{12}$
$\text{Model Diameter} = 17.5$ mm

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Problem 17: Error Analysis

Step1: Identify proportion error

The scale is $\frac{1\ \text{cm}}{20\ \text{m}}$, so the correct proportion is $\frac{1\ \text{cm}}{20\ \text{m}} = \frac{5\ \text{cm}}{x\ \text{m}}$ (the original inverted the scale ratio).

Step2: Solve for correct actual distance

$x = 20 \times 5$
$x = 100$ m

Answer:

1. 75 in.
2. 15 in.
3. 3.84 m
4. 21.6 yd
5. 17.5 mm
6. The error is inverting the scale ratio in the proportion. The correct actual distance is 100 m.