The only "Egyptian" pyramid in Europe

Geometry Level pending

The above photo is the Pyramid of Cestius in Rome, Italy. It has a square base with edge length of 98.4 feet. If the volume is 392143.68 cubic feet, find it's slant height in feet correct to two decimal places.


The answer is 131.08.

A Former Brilliant Member by A Former Brilliant Member

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1 solution

The volume of a regular pyramid is given by: V = 1 3 A b h V=\dfrac{1}{3}A_bh where A b A_b = area of the base and h h = height.

Substituting, we get

392143.68 = 1 3 ( 98.4 ) 2 ( h ) 392143.68=\dfrac{1}{3}(98.4)^2(h)

h = 121.5 h=121.5

Note that the slant height is the altitude of a lateral face. So by pythagorean theorem , we have

L = 121. 5 2 + ( 98.4 2 ) 2 = L=\sqrt{121.5^2+\left(\dfrac{98.4}{2}\right)^2}= 131.08 \color{#D61F06}\large \boxed{131.08}

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