Question

Find the scale factor of the two pyramids, the ratio of their surface areas, and the ratio of theirvolumes. List the larger values first. Simplify all ratios.12 ft24 ft9 ft212 ft9 ft18 ftScale FactorSurface AreasVolumesBlank 1:Blank 2:Blank 3:Blank 4:Blank 5:Blank 6:

Answer 1

We will solve as follows:

*Scale factor:

We determine the scale factor by using one of the sides of the base of each pyramid:

`12x=9\Rightarrow x=(9)/(12)\Rightarrow x=(3)/(4)`

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:

`A_1=(12\cdot12)+4((12\cdot24)/(2))\Rightarrow A_1=720`
`A_2=(9\cdot9)+4((9\cdot18)/(2))\Rightarrow A_2=405`

Now:

`720x=405\Rightarrow x=(405)/(720)\Rightarrow x=(9)/(16)`

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:

`V_1=(1)/(3)(12)^2\cdot(24)\Rightarrow V_1=1152`
`V_2=(1)/(3)(9)^2\cdot(18)=V_2=486`

Now:

`1152x=486\Rightarrow x=(486)/(1152)\Rightarrow x=(27)/(64)`

So, the ratio of the volumes is 27: 64.