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?

Answer 1

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 $\iff$ 0.512 L

Length Length
5 m $\iff$ $?$ m

Ratio of corresponding values = $\frac{64L}{0.512L}=125$

Volume = Length $\times$ Width $\times$ Height

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

Volume = length $\times$ length $\times$ length
Volume = length ${}^3$
So, Length = (Volume)${}^{\frac{1}{3}}$
Length = (125)${}^{\frac{1}{3}}$ m
Length = 5 m

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