Question 1

We will measure the actual dimensions of the classroom and its objects, then convert them to scaled dimensions using the given ratio.

Step 1 — Measure Actual Classroom Dimensions

Let us first measure the actual length and width of the classroom. We will assume a typical classroom size for this example.

Let the actual length of the classroom be $L_{\text{actual}}$. Let the actual width of the classroom be $W_{\text{actual}}$.

$L_{\text{actual}} = 10 \text{ meters}$

$L_{\text{actual}} = 10 \times 100 \text{ cm}$

$= 1000 \text{ cm}$

$W_{\text{actual}} = 8 \text{ meters}$

$W_{\text{actual}} = 8 \times 100 \text{ cm}$

$\boxed{= 800 \text{ cm}}$

Step 2 — Calculate Scaled Classroom Dimensions

The given scale is 1:50. This means 1 unit on the map represents 50 units in reality. To find the map dimension, we divide the actual dimension by 50.

Let the scaled length of the classroom be $L_{\text{map}}$. Let the scaled width of the classroom be $W_{\text{map}}$.

$L_{\text{map}} = \frac{L_{\text{actual}}}{50}$

$L_{\text{map}} = \frac{1000 \text{ cm}}{50}$

$= 20 \text{ cm}$

$W_{\text{map}} = \frac{W_{\text{actual}}}{50}$

$W_{\text{map}} = \frac{800 \text{ cm}}{50}$

$\boxed{= 16 \text{ cm}}$

Step 3 — Measure and Scale Object Dimensions and Positions

We will assume positions and dimensions for various objects in the classroom. We will use one corner of the classroom as the origin $(0,0)$ for our measurements.

• Blackboard:

  • Actual width: $3 \text{ m} = 300 \text{ cm}$.
  • Scaled width: $300 \text{ cm} / 50 = \mathbf{6 \text{ cm}}$.
  • Actual position: Centered on the $8 \text{ m}$ wall (from $2.5 \text{ m}$ to $5.5 \text{ m}$ along the wall).
  • Scaled position: From $250 \text{ cm} / 50 = \mathbf{5 \text{ cm}}$ to $550 \text{ cm} / 50 = \mathbf{11 \text{ cm}}$ along the front wall.

• Teacher's Desk:

  • Actual dimensions: $1.5 \text{ m}$ (length) $\times 0.75 \text{ m}$ (width).
  • Scaled dimensions: $(150 \text{ cm} / 50) \times (75 \text{ cm} / 50) = \mathbf{3 \text{ cm} \times 1.5 \text{ cm}}$.
  • Actual position: Top-left corner at $(2 \text{ m}, 1 \text{ m})$ from the origin.
  • Scaled position: $(200 \text{ cm} / 50, 100 \text{ cm} / 50) = \mathbf{(4 \text{ cm}, 2 \text{ cm})}$.

• Fans:

  • Actual diameter: $1.2 \text{ m} = 120 \text{ cm}$.
  • Scaled diameter: $120 \text{ cm} / 50 = \mathbf{2.4 \text{ cm}}$.
  • Actual positions (centers): Fan 1 at $(4 \text{ m}, 2.5 \text{ m})$, Fan 2 at $(4 \text{ m}, 7.5 \text{ m})$.
  • Scaled positions (centers): Fan 1 at $(400/50, 250/50) = \mathbf{(8 \text{ cm}, 5 \text{ cm})}$. Fan 2 at $(400/50, 750/50) = \mathbf{(8 \text{ cm}, 15 \text{ cm})}$.

• Lights:

  • Actual dimensions: $0.6 \text{ m} \times 0.15 \text{ m} = 60 \text{ cm} \times 15 \text{ cm}$.
  • Scaled dimensions: $(60/50) \text{ cm} \times (15/50) \text{ cm} = \mathbf{1.2 \text{ cm} \times 0.3 \text{ cm}}$.
  • Actual positions (centers): L1 $(2 \text{ m}, 1.5 \text{ m})$, L2 $(6 \text{ m}, 1.5 \text{ m})$, L3 $(2 \text{ m}, 8.5 \text{ m})$, L4 $(6 \text{ m}, 8.5 \text{ m})$.
  • Scaled positions (centers): L1 $\mathbf{(4 \text{ cm}, 3 \text{ cm})}$, L2 $\mathbf{(12 \text{ cm}, 3 \text{ cm})}$, L3 $\mathbf{(4 \text{ cm}, 17 \text{ cm})}$, L4 $\mathbf{(12 \text{ cm}, 17 \text{ cm})}$.

• Student Desks:

  • Actual dimensions: $1.2 \text{ m} \times 0.6 \text{ m} = 120 \text{ cm} \times 60 \text{ cm}$.
  • Scaled dimensions: $(120/50) \text{ cm} \times (60/50) \text{ cm} = \mathbf{2.4 \text{ cm} \times 1.2 \text{ cm}}$.
  • Actual positions (top-left corners): SD1 $(1 \text{ m}, 3 \text{ m})$, SD2 $(3 \text{ m}, 3 \text{ m})$, SD3 $(1 \text{ m}, 5 \text{ m})$, SD4 $(3 \text{ m}, 5 \text{ m})$, SD5 $(1 \text{ m}, 7 \text{ m})$, SD6 $(3 \text{ m}, 7 \text{ m})$.
  • Scaled positions (top-left corners): SD1 $\mathbf{(2 \text{ cm}, 6 \text{ cm})}$, SD2 $\mathbf{(6 \text{ cm}, 6 \text{ cm})}$, SD3 $\mathbf{(2 \text{ cm}, 10 \text{ cm})}$, SD4 $\mathbf{(6 \text{ cm}, 10 \text{ cm})}$, SD5 $\mathbf{(2 \text{ cm}, 14 \text{ cm})}$, SD6 $\mathbf{(6 \text{ cm}, 14 \text{ cm})}$.

• Door:

  • Actual width: $1 \text{ m} = 100 \text{ cm}$.
  • Scaled width: $100 \text{ cm} / 50 = \mathbf{2 \text{ cm}}$.
  • Actual position: From $0 \text{ m}$ to $1 \text{ m}$ along the front wall.
  • Scaled position: From $\mathbf{0 \text{ cm}}$ to $\mathbf{2 \text{ cm}}$ along the front wall.

Step 4 — Choose Symbols and Sketch the Map

We will use simple symbols to represent the objects on our map.

• Classroom Walls: Thick lines forming a rectangle.
• Blackboard: A thick rectangle on the wall.
• Teacher's Desk: A rectangle with a 'T' inside.
• Fan: A circle with an 'X' inside.
• Light: A small rectangle with an 'L' inside.
• Student Desk: A small rectangle.
• Door: A gap in the wall.

Answer

(i) The classroom map will be a rectangle of 20 cm length and 16 cm width. (ii) The teacher's desk will be a rectangle of 3 cm length and 1.5 cm width on the map. (iii) Fans will be represented by circles with a diameter of 2.4 cm on the map.