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How heavy is 365,000 tons?

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It's about as heavy as The Empire State Building.
(New York City, New York)
The Empire State Building weighs approximately 365,000 tons. About 4% of the building's weight is its 6,000 cu. m (200,000 cu. ft) of limestone façade.
It's about one-and-two-thirds times as heavy as The Sears Tower.
In other words, 365,000 tons is 1.6410 times the weight of The Sears Tower, and the weight of The Sears Tower is 0.60940 times that amount.
(officially "Willis Tower" as of 2009) (Chicago, Illinois)
The Willis Tower weighs approximately 222,400 tons. The outer wall surface of the Tower is covered with black anodized aluminum panels which would total 110,000 sq. m (28 acres) if laid out together.
It's about two-fifths as heavy as The Golden Gate Bridge.
In other words, 365,000 tons is 0.4110 times the weight of The Golden Gate Bridge, and the weight of The Golden Gate Bridge is 2.430 times that amount.
(San Francisco, California and Marin County, California) (Post 1986 weight reduction; total weight of bridge, anchorage, and approaches)
Following the completion of the 1986 project to eliminate excess material, the total weight of the Golden Gate Bridge — including its anchorages and approaches — is 887,000 tons. The two main cables in the spanning the bridge are spun out of a total of 129,000 km (80,200 mi) of wire.
It's about three times as heavy as The CN Tower.
In other words, 365,000 tons is 2.80830 times the weight of The CN Tower, and the weight of The CN Tower is 0.356090 times that amount.
(a.k.a. La Tour CN, a.k.a. Canadian National Tower, a.k.a. Canada's National Tower) (Toronto, Canada)
The CN Tower weighs approximately 129,970 tons. The Tower is home to the world's highest glass floor — a viewing area that allows visitors to look straight down 342 m (1,120 ft) to the ground below.
It's about thirteen-and-a-half times as heavy as The Statue of Liberty.
In other words, the weight of The Statue of Liberty is 0.0746 times 365,000 tons.
(a.k.a. Liberty Enlightening the World, a.k.a. La Liberté éclairant le monde) (total weight, including foundation)
The total weight of the Statue of Liberty, including her base is roughly 27,100 tons. The statue was designed using an optical trick known as "forced perspective" to make the statue appear proportionally correct when viewed from its base and is, in actuality, disproportionately large at the top.
It's about one-twentieth as heavy as The Great Pyramid of Giza.
In other words, the weight of The Great Pyramid of Giza is 18 times 365,000 tons.
(a.k.a. Pyramid of Khufu, a.k.a. Pyramid of Cheops) (Cairo, Egypt)
The Great Pyramid of Giza has an estimated mass of 6,500,000 tons. The 2,300,000 stones used in the construction of the pyramid weighed an average 2.50 tons and were quarried from distances of up to 805 km (500 mi) away.
It's about twenty times as heavy as The Brooklyn Bridge.
In other words, 365,000 tons is 24.860 times the weight of The Brooklyn Bridge, and the weight of The Brooklyn Bridge is 0.04023 times that amount.
(a.k.a. New York and Brooklyn Bridge) (Manhattan and Brooklyn, New York City, New York) (total weight)
The total weight of the Brooklyn Bridge is approximately 14,680 tons. In a promotional event to prove the bridge's stability shortly after it opened, entertainer P. T. Barnum led a parade of 21 elephants across it in May of 1884.