A scale model of a statue is made using a scale of \(1 : 12\). The model is \(27.5\) cm tall. Calculate the height of the real statue, in metres.
Question 1 Report
A scale model of a statue is made using a scale of \(1 : 12\).
The model is \(27.5\) cm tall.
Calculate the height of the real statue, in metres.
Answer Details
The scale \( 1 : 12 \) means that \( 1 \) cm on the model represents \( 12 \) cm on the real statue, so the real object is found by multiplying the model measurement by \( 12 \).
- Multiply by the scale factor: \[ 27.5 \times 12 = 330 \text{ cm} \] [M1]
- Convert to metres, as the question requires: \( 330 \div 100 = 3.3 \) m.
The real statue is \( 3.3 \) m tall. [A1]
Because the model was measured in centimetres, the product is also in centimetres; the ratio itself has no unit and never changes the unit you are working in. Converting only at the very end keeps the arithmetic simple and avoids dividing by \( 100 \) at the wrong point.
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