Volume and surface area of "One World Trade Center"

[Hyydrxzen]

Hi to everyone,
do you know the "One World Trade Center"?

Well, I've to calculate two things about it:

-The volume, according to its particular shape
-The surface of the glass plates which cover the whole structure

Searching on internet i found two dimensions:
1) Total height without antenna: 417 m
2) Cubic base dimensions: 61 m, for every side

Thanks for your attention, I hope you will see this message!

 

[MarkFL]

Hello, and welcome to MHB! :)

I found this online:

"The new shape plays with geometry and perceptions. The base is a 200ft x 200ft (61m x 61m) square and the first 20 storeys rise straight up, aligned with this square. The design was revised twice in June 2005 and in June 2006 to cover the concrete base with a screen of glass prisms.

From the 20th floor up to a 1,368ft-high parapet, the edges chamfer back, creating eight triangular planes. The square rotates until the 102nd-floor square has turned 45° from the square on the 20th floor.

The eight, elongated, isosceles triangles form a neat configuration on the façade. These alternate between triangles with the apex on the 102nd floor and those with the apex at the 20th floor. The downward-facing triangles slope inward slightly, which is to say that the footprint of each floor shrinks slightly at higher points."

One could likely use the calculus to compute the volume, but without more details regarding the slight inward slope of the downward facing triangles it wouldn't be very accurate.

 

[Hyydrxzen]

The result is not important, I only need to point a result according to the infos that I have and focus on the method.

 

[topsquark]

The result is not important, I only need to point a result according to the infos that I have and focus on the method.

He's telling you that you need more information to solve the problem. As the tower is not a rectangular solid it can't be done with the information you were given.

-Dan

 

[Hyydrxzen]

I could suppose that the building is a rectangular solid put on a cubic base

 

[Jameson]

I could suppose that the building is a rectangular solid put on a cubic base

Ok this is a good start. What do we know or can assume then go further? Your post is a statement that doesn’t use equations about what the answer is asking. Now you can take the verbal idea and translate that to math. What are the pieces of this from your sentence? What is known or not? How do these things all connect with an equal’s sign.

 

[itsdesm]

The YouTube channel "Stand up maths" just posted a video calculating this. Their answer is ~39 million cubic feet