Since the volume of the small pyramid is 1×10-9 times the volume of the big pyramid, then the slant height of the small pyramid is 1×10-3 times the slant height of the big pyramid. Hence the slant height is 300*1×10-3 = 0.3m = 30cm. This is because both pyramids have the exact same dimensions just on a different scale. Thus when you multiply all the lengths of the small pyramid by 10^3, you end up getting a volume that is larger by 10^9, which is 10^3 cubed since volume scales by the cube of lengths. You can work it out with the exact values to confirm this.

part 2: by the same logic, the surface area of the big pyramid is 10^6 larger than the surface area of the small pyramid, because area scales by the square of lengths. Thus the fraction is 1000000/1=1×10^6 in standard form. Again you can work it out with the actual values to confirm. Hope this helps!

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Thank you for help with detailed explanation.  

Thanks!

It says the model is 1×10(-9) times of the WEIGHT of the actual pyramid, though.  I’m not sure if we can use weight as a matter of dimensional proportions, though.  Oh well, there is no other way.

In this case you can use volume as a substitute for weight, because the question said that both pyramids are made of the same material, so 1×10-9 times the weight also means 1×10-9 times the volume.