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Question



A car manufacturer also produces exact scale models of the cars. The fuel tank of the real car has a volume of 64 liters, and that of the model car has a volume of 0.512 liters. If the length of the real car is 5 meters , what is the length of the model car?

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Solution

The fuel tank of the real car has a volume = 64 liters
The fuel tank of the real car has a volume of 64 liters, and that of the model car has a volume of 0.512 liters



REAL MODEL
64 L 0.512 L

Length Length
5 m ? m

Ratio of corresponding values = 64L0.512L=125

Volume = Length × Width × Height

To find how the relative lengths are changing, we need to find cube root of ratio of volume of fuel tank.

Volume = length × length × length
Volume = length 3
So, Length = (Volume)13
Length = (125)13 m
Length = 5 m

Length that corresponds to the given volume:
Real car Model car
Volume 125 : 1
Length 5 : 1
the length of the model car would be 1 m.


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