Question

The sides of the base of the largest pyramid, Khufu, has length 755 ft. The height of Khufu was originally 482 ft but is now 450 ft. What is the length of the slope of a side of the pyramid at its original size and its present size?

Answer 1

Khufu

The pyramid has square base of length `l=755ft`
and it had original height `h_o=482ft`
It present height `h_p=450ft`

The length of the slope of a side of the pyramid at its original size

`S_"original"=sqrt(h_o^2+(l/2)^2)=sqrt(482^2+(755/2)^2)=612.23ft`

[The length of the slope of a side of the pyramid at its present size

`S_"present"=sqrt(h_p^2+(l/2)^2)=sqrt(450^2+(755/2)^2)=587.37ft`

This calculation of Slant height is not valid if top is not a point.]

Other calculation :

If x is the slant height diminished due to flattened top,then by the property of similar triangles we can write

`"Slant height diminished"/"Original slant height"="Height diminished"/"Original height"`

`=>x/612.23=(482-450)/482`

`=>x=32/482*612.23=40.64ft`

So at present the slant height becomes`=612.23-40.64=571.59ft`