Math Problem Statement

A walk by the river measures 10.cm on a map which has the scale of 1 : 25000. Calculate the distance covered on the ground in KM and to two significant figures

Solution

To find the actual distance on the ground, we will use the map scale, which is 1 : 25,000. This means that 1 cm on the map represents 25,000 cm in reality.

  1. Convert the map measurement to the real distance:

    Actual distance=10cm×25,000=250,000cm\text{Actual distance} = 10 \text{cm} \times 25,000 = 250,000 \text{cm}

  2. Convert centimeters to kilometers:

    Since there are 100,000 cm in a kilometer:

    Distance in kilometers=250,000cm100,000=2.5km\text{Distance in kilometers} = \frac{250,000 \text{cm}}{100,000} = 2.5 \text{km}

The distance covered on the ground is 2.5 km, which is already to two significant figures.

Would you like further details or have any questions?

Here are five related questions:

  1. How would the calculation change if the map scale was 1 : 50,000?
  2. What is the distance in meters instead of kilometers?
  3. How do you convert different map scales to real distances?
  4. If the scale was 1 : 10,000, how far would 10 cm on the map be on the ground?
  5. What if the measurement was in inches; how would the conversion proceed?

Tip: Always ensure that units are consistent throughout your calculations to avoid errors.

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Math Problem Analysis

Mathematical Concepts

Geometry
Scale Conversion
Unit Conversion

Formulas

Actual distance = Map distance × Scale factor
Distance in kilometers = Distance in cm / 100,000

Theorems

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Suitable Grade Level

Grades 6-8