Question

The area of plan is 10 cm\(^2\) drawn to a scale of 1 cm = 10m. The area measured on the ground is

• A. 200 m\(^2\)
• B. 2000 m\(^2\)
• C. 100 m\(^2\)
• D. 1000 m\(^2\)

Hint:

A common mistake is to forget to square the scale factor when converting areas.
Remember: for lengths, use the scale directly.
For areas, use the square of the scale.
For volumes, use the cube of the scale.

Answer 1

The Correct Option is D

Step 1: Understanding the Question:
We are given an area on a plan and the linear scale of the plan.
We need to calculate the corresponding actual area on the ground.

Step 2: Key Formula or Approach:
First, we need to convert the linear scale to an area scale.
If the linear scale is 1 unit (plan) = n units (ground), then the area scale is (1 unit)\(^2\) (plan) = n\(^2\) units\(^2\) (ground).
Then, multiply the plan area by the area scale factor to get the ground area.

Step 3: Detailed Explanation:
The given linear scale is:
\[ 1 \, \text{cm} = 10 \, \text{m} \] To find the area scale, we square both sides of this relationship:
\[ (1 \, \text{cm})^2 = (10 \, \text{m})^2 \] \[ 1 \, \text{cm}^2 = 100 \, \text{m}^2 \] This means that one square centimeter on the plan represents 100 square meters on the ground.
The area of the plan is given as 10 cm\(^2\).
To find the corresponding ground area, we multiply the plan area by the area scale factor:
\[ \text{Ground Area} = 10 \, \text{cm}^2 \times \frac{100 \, \text{m}^2}{1 \, \text{cm}^2} = 1000 \, \text{m}^2 \]

Step 4: Final Answer:
The area measured on the ground is 1000 m\(^2\).
This corresponds to option (D).