The model of a building is constructed with the scale factor `1:30`.
(i) If the height of the model is 80 cm, find the actual height of the building in metres.

Answer

To solve the problem step by step, we will follow these instructions:

### Step 1: Understand the scale factor
The scale factor given is 1:30. This means that 1 unit on the model corresponds to 30 units in reality.

### Step 2: Convert the height of the model to meters
The height of the model is given as 80 cm. To convert this to meters, we use the conversion factor where 1 meter = 100 cm.

\[ \text{Height of the model in meters} = \frac{80 \text{ cm}}{100} = 0.8 \text{ meters} \]

### Step 3: Set up the proportion using the scale factor
Let the actual height of the building be \( X \) meters. According to the scale factor, we can set up the following proportion:

\[ \frac{\text{Height of the model}}{\text{Actual height}} = \frac{1}{30} \]

Substituting the known values:

\[ \frac{0.8}{X} = \frac{1}{30} \]

### Step 4: Cross-multiply to solve for \( X \)
Cross-multiplying gives us:

\[ 0.8 \times 30 = 1 \times X \]

This simplifies to:

\[ X = 0.8 \times 30 \]

### Step 5: Calculate the actual height
Now, we can calculate \( X \):

\[ X = 24 \text{ meters} \]

### Final Answer
The actual height of the building is **24 meters**.

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