Math Problem Statement

44

A city is planning to place a 22-foot-high statue in a local park. The artist who earned the commission is working from a model that is 18 inches high. A feature on the model measures 3 inches across. How large will the feature on the completed statue be?

Solution

Let's solve question 44:

The problem involves scaling up the size of a feature from a model to a statue.

Given:

  • Model height = 18 inches
  • Feature on model = 3 inches
  • Statue height = 22 feet
    Convert 22 feet to inches:
    22×12=264 inches22 \times 12 = 264 \text{ inches}

We assume the statue and model are proportional, so the scaling factor is: Scaling Factor=Statue heightModel height=26418=14.67\text{Scaling Factor} = \frac{\text{Statue height}}{\text{Model height}} = \frac{264}{18} = 14.67

Scale up the feature:

The size of the feature on the statue is: Feature size=Feature on model×Scaling Factor\text{Feature size} = \text{Feature on model} \times \text{Scaling Factor} Feature size=3×14.67=44.01 inches\text{Feature size} = 3 \times 14.67 = 44.01 \text{ inches}

Convert this back to feet: 44.01inches÷12=3.67feet44.01 \, \text{inches} \div 12 = 3.67 \, \text{feet}

Final Answer:

The feature on the statue will be approximately 3.67 feet.
Correct option: B.


Do you want me to clarify any step further or explain another question?

Related Questions:

  1. How do you convert feet to inches and vice versa?
  2. How would the scaling factor change if the statue were 30 feet tall?
  3. If another feature on the model was 5 inches, what would its size be on the statue?
  4. What is the importance of proportional scaling in art and design?
  5. How would the problem change if the model was measured in centimeters?

Tip:

Always double-check unit conversions, especially when dealing with feet, inches, or metric measurements!

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Math Problem Analysis

Mathematical Concepts

Proportionality
Scaling Factors
Unit Conversion

Formulas

Scaling Factor = Statue Height / Model Height
Feature Size on Statue = Feature Size on Model × Scaling Factor
Feet to Inches Conversion: 1 foot = 12 inches

Theorems

Proportional Scaling Theorem

Suitable Grade Level

Grade 6-8