Answer:
[tex]\frac83; \frac{512}{27}; 14\ 222.222 m^3[/tex]
Step-by-step explanation:
In general, if in two similar solids the corrisponding linear measure (same side, same diagonal, etc) are in a ratio of K, surface measures will be in a ratio of [tex]K^2[/tex] and volumes will be in a ratio of [tex]K^3[/tex]. We know the ratio of the surfaces, so we can say that
[tex]K^2 = \frac{320}{45} = \frac{64}9[/tex]
1. the ratio of the scale factor can be easily found by the ratio of the surfaces, and it's [tex]K= \sqrt{K^2} = \sqrt{\frac{64}{9}} = \frac83[/tex]
2. The ratio of the volumes is the cube of the ratio we just found:
[tex]K^3 = (\frac83)^3 =\frac{512}{27}[/tex]
3. to find the volume of the larger solid you just multiply the ratio we found in the last point by the volume of the smaller solid.
[tex]V=750m^3\times \frac{512}{27} = \frac{128\ 000}{9} m^3 \approx 14\ 222.222 m^3[/tex]
