If the diameter of a scaled-down model of the Earth is 45 cm, then the equivalent length on the surface of the Earth for 1 cm on the model is _____________ km (rounded off to two decimal places).
[Use: Radius of the Earth = 6371 km]
[Use: Radius of the Earth = 6371 km]
Show Hint
Correct Answer: 283.16
Solution and Explanation
We are given the radius of the Earth as \(6371\) km. The diameter is twice the radius, so
\[ D_{earth} = 2 \times 6371 = 12742 \text{ km} \]
Step 2: Set up the scale ratio.
The scaled-down model has a diameter of \(45\) cm, and this \(45\) cm represents the full \(12742\) km of the real Earth. The scale of the model is therefore
\[ \text{Scale} = \frac{12742 \text{ km}}{45 \text{ cm}} \]
Step 3: Find the length represented by 1 cm.
Dividing both sides by \(45\), the length on the real Earth equivalent to \(1\) cm on the model is
\[ \frac{12742}{45} = 283.1555... \text{ km} \]
Step 4: Round to two decimal places.
Rounding \(283.1555\) to two decimal places gives
\[ 283.16 \text{ km} \]
Step 5: Final conclusion.
So 1 cm on the scaled-down model equals about \(283.16\) km on the actual surface of the Earth. This value lies within the accepted range of \(283.00\) to \(283.25\) km.
\[ \boxed{283.16 \text{ km}} \]
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