We are supposed to find the distance between sun and earth of the given model, where sun's diameter is given to be 65 cm.
Let the model's distance between Earth and Sun be x.
To find the model's distance between sun and earth we can set an equation of the given information.
[tex]\frac{\text{Diameter in the model}}{\text{Distance in the model}}=\frac{\text{Actual diameter}}{\text{Actual distance}}[/tex]
[tex]\frac{65}{x}=\frac{1.4\times 10^{9}}{1.5\times 10^{11}}[/tex]
Now let us solve for x.
[tex]x=\frac{65\cdot (1.5\times 10^{11})}{1.4\times 10^{9}}[/tex]
[tex]=\frac{65\times 1.5\times 10^{11}}{1.4\times 10^{9}}[/tex]
[tex]=\frac{97.5\times 10^{11}}{1.4\times 10^{9}}[/tex]
[tex]=\frac{97.5\times 10^{(11-9)}}{1.4}[/tex]
[tex]=\frac{97.5\times 10^{2}}{1.4} =\frac{9750}{1.4}[/tex]
[tex]=6964.2857[/tex]
Therefore, model's distance between Earth and Sun is 6964.29 centimeters.
