https://file.aiquickdraw.com/mathbot/file/1727442010645kdalzpln.jpg

Let's work through this problem step by step.

### Problem Overview:
- **Scale diagram height**: 3 cm
- **Real-life building height**: 45 m
- Ben is trying to find the ratio but seems to have made a mistake.

### Part (a) - Explaining Ben's Mistake:
The mistake Ben likely made is not converting the units properly before calculating the ratio. The heights given are in different units: the diagram uses **centimeters (cm)**, while the real-life building is measured in **meters (m)**. To work out the scale, both measurements should be in the same unit.

Ben probably compared the 3 cm from the scale diagram directly to the 45 meters of the real building, which is incorrect. The correct approach is to convert the 45 meters to centimeters before finding the ratio, as both should be in centimeters.

### Part (b) - Calculating the Correct Ratio:
To get the correct ratio:
1. Convert 45 meters to centimeters. Since 1 meter = 100 centimeters:
   \[
   45 \, \text{m} = 45 \times 100 = 4500 \, \text{cm}
   \]

2. Now the two heights are:
   - Scale diagram height: 3 cm
   - Real-life height: 4500 cm

3. The ratio of the diagram height to the real height is:
   \[
   \text{Ratio} = \frac{3 \, \text{cm}}{4500 \, \text{cm}} = \frac{1}{1500}
   \]
   
So, the correct ratio is **1:1500**.

Would you like to explore further details or ask any questions?

---

### Related Questions:
1. How do you convert between different units of measurement?
2. What are the other common ratios used in scale drawings?
3. How do you simplify a ratio to its simplest form?
4. What happens if you don't convert units properly when working with ratios?
5. Can the same method be applied to 3D objects like volume ratios?

**Tip**: Always make sure all quantities are in the same unit before comparing or calculating ratios!

A scale diagram of a building has a height of 3 cm. The real-life building has a height of 45 m. Ben has tried to work out the scale of the diagram as a ratio in its simplest form. Write a sentence to explain the mistake Ben has made. Work out the correct ratio.

Learn how to solve a scale ratio problem involving a building height comparison between a diagram and real-life. The problem focuses on converting meters to centimeters and simplifying ratios to their simplest form. Suitable for Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation