We will solve as follows:
*Scale factor:
We determine the scale factor by using one of the sides of the base of each pyramid:
[tex]12x=9\Rightarrow x=\frac{9}{12}\Rightarrow x=\frac{3}{4}[/tex]
So, the scale factor is of 3 : 4.
*Surface areas:
We determine the surface area for each pyramid and proceed in a similar fashion as the previous point:
[tex]A_1=(12\cdot12)+4(\frac{12\cdot24}{2})\Rightarrow A_1=720[/tex][tex]A_2=(9\cdot9)+4(\frac{9\cdot18}{2})\Rightarrow A_2=405[/tex]
Now:
[tex]720x=405\Rightarrow x=\frac{405}{720}\Rightarrow x=\frac{9}{16}[/tex]
So, the ratio of surface areas is 9 : 16.
*Volumes:
Ve determine the volume of each pyramid and proceed in a similar fashion asn the previous points:
[tex]V_1=\frac{1}{3}(12)^2\cdot(24)\Rightarrow V_1=1152[/tex][tex]V_2=\frac{1}{3}(9)^2\cdot(18)=V_2=486[/tex]
Now:
[tex]1152x=486\Rightarrow x=\frac{486}{1152}\Rightarrow x=\frac{27}{64}[/tex]
So, the ratio of the volumes is 27: 64.
