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How heavy is 0.0101 megatonnes?

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It's about as heavy as The Eiffel Tower.
(a.k.a. La Tour Eiffel) (Paris, France) (total weight)
The Eiffel Tower weighs approximately 0.0101 megatonnes. Architected to be quickly assembled, the Tower contains only 930 cu. meters of solid material.
It's about three-fourths as heavy as The Brooklyn Bridge.
In other words, 0.0101 megatonnes is 0.75830 times the weight of The Brooklyn Bridge, and the weight of The Brooklyn Bridge is 1.3190 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 0.01332 megatonnes. 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 two-fifths as heavy as The Statue of Liberty.
In other words, 0.0101 megatonnes is 0.410 times the weight of The Statue of Liberty, and the weight of The Statue of Liberty is 2.440 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 0.0246 megatonnes. 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 eight times as heavy as a Tree (Sierra Redwood).
In other words, 0.0101 megatonnes is 7.80 times the weight of a Tree (Sierra Redwood), and the weight of a Tree (Sierra Redwood) is 0.130 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 0.0013 megatonnes. 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 0.0019 megatonnes.
It's about one-tenth as heavy as The CN Tower.
In other words, 0.0101 megatonnes is 0.085659 times the weight of The CN Tower, and the weight of The CN Tower is 11.6740 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 0.117910 megatonnes. 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 sixteen times as heavy as Christ the Redeemer (statue).
In other words, 0.0101 megatonnes is 15.90 times the weight of Christ the Redeemer (statue), and the weight of Christ the Redeemer (statue) is 0.0629 times that amount.
(a.k.a. O Cristo Redentor, a.k.a. Christo redemptor) (Rio de Janeiro, Brazil)
Christ the Redeemer weighs 0.000635 megatonnes. 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 one-twentieth as heavy as The Sears Tower.
In other words, 0.0101 megatonnes is 0.05005 times the weight of The Sears Tower, and the weight of The Sears Tower is 19.980 times that amount.
(officially "Willis Tower" as of 2009) (Chicago, Illinois)
The Willis Tower weighs approximately 0.20180 megatonnes. 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.