1. Let [tex]A_1[/tex] and [tex]A_2[/tex] be the areas of 2 similar figures.
Similar figures have a scale factor k, (let k be >1, so k is the ratio of a distance in the larger figure to the corresponding distance in the smaller one)
The ratio of the area of the larger figure to the area of the smaller is [tex] k^{2} [/tex]
The ratio of the volume of the larger figure to the volume of the smaller is [tex] k^{3} [/tex]
2. [tex] \frac{A_2}{A_1}= \frac{25}{16}= \frac{ 5^{2} }{ 4^{2} }= ( \frac{5}{4} )^{2} [/tex]
so k is 5/4
3.
[tex] \frac{V_2}{V_1} = \frac{500}{V_1}= ( \frac{5}{4} )^{3}= \frac{125}{64} [/tex]
[tex]\frac{500}{V_1}= \frac{125}{64} [/tex]
[tex]V_1= \frac{500*64}{125}= 4*64=256[/tex] in cubed
