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How heavy is 4,000 tonnes?

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It's about two-fifths as heavy as The Eiffel Tower
In other words, 4,000 tonnes is 0.396 times the weight of The Eiffel Tower, and the weight of The Eiffel Tower is 2.53 times that amount.
(a.k.a. La Tour Eiffel) (Paris, France) (total weight)
The Eiffel Tower weighs approximately 10,100 tonnes. Architected to be quickly assembled, the Tower contains only 930 cu. meters of solid material.
It's about three times as heavy as a Tree (Sierra Redwood)
In other words, 4,000 tonnes is 3.1 times the weight of a Tree (Sierra Redwood), and the weight of a Tree (Sierra Redwood) is 0.32 times that amount.
(a.k.a. Giant Sequoia, a.k.a. Sierran redwood, a.k.a. Wellingtonia, a.k.a. "Big Tree", Sequoiadendron giganteum)
The weight of wood in a Giant Sequoia is 1,300 tonnes. General Sherman, a specimen in Sequoia National Park in Visalia, California, is the largest tree in the world by volume, with an estimated weight of about 1,900 tonnes.
It's about three-tenths as heavy as The Brooklyn Bridge
In other words, 4,000 tonnes is 0.3003 times the weight of The Brooklyn Bridge, and the weight of The Brooklyn Bridge is 3.33 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 13,320 tonnes. 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.
It's about one-fifth as heavy as The Statue of Liberty
In other words, 4,000 tonnes is 0.162 times the weight of The Statue of Liberty, and the weight of The Statue of Liberty is 6.17 times that amount.
(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 24,600 tonnes. 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 six-and-a-half times as heavy as Christ the Redeemer (statue)
In other words, 4,000 tonnes is 6.3 times the weight of Christ the Redeemer (statue), and the weight of Christ the Redeemer (statue) is 0.159 times that amount.
(a.k.a. O Cristo Redentor, a.k.a. Christo redemptor) (Rio de Janeiro, Brazil)
Christ the Redeemer weighs 635 tonnes. The statue overlooks the city of Rio de Janeiro from atop the 709.9-meter (2,329 ft) granite peak in the Tijuca Forest National Park.
It's about thirty times as heavy as a House
In other words, 4,000 tonnes is 25.6 times the weight of a House, and the weight of a House is 0.039 times that amount.
(149 sq. m, single-level, unfurnished)
A 149 sq. m (1,600 sq. ft), single-story, unfurnished house (without extensive masonry) of the type commonly found in America would weigh approximately 156 tonnes, based on the weight of the included materials. In contrast, a yurt — a type of dwelling structure popular among nomadic peoples of East Asia — typically weighs less than 0.460 tonnes.
It's about thirty times as heavy as The Statue of Liberty (without base)
In other words, 4,000 tonnes is 29 times the weight of The Statue of Liberty (without base), and the weight of The Statue of Liberty (without base) is 0.03 times that amount.
(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 — the Statue's copper and framework only, excluding the base — is roughly 140 tonnes. 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.