Question 442768
a) A locomotive is 10 m long and weighs 72 tonnes. A similar model, made of the same material, is 40 cm long, find the mass of the model.
:
Convert 40 cm to .4 m
:
Use a volume proportion equation, let x = mass of the 40 cm engine
{{{x/72}}}= {{{.4^3/10^3}}}
{{{x/72}}}= {{{.064/1000}}}
Cross multiply:
1000x = 72 * .064
1000x = 4.608
x = {{{4.608/1000}}}
x = .004608 tonnes
change to kilograms
.004608*1000 = 4.61 kg
:
:
b) Suppose the tank of the model locomotive contains 0.85 liters of water when full, find the capacity of the tank of the locomotive.
{{{.85/x}}}= {{{.064/1000}}}
.064x = 1000*.85
.064x = 850
x = {{{850/.064}}}
x = 13,281.25 liters of water