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How heavy is 646 tons?

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It's about nine-tenths as heavy as Christ the Redeemer (statue).
In other words, 646 tons is 0.923 times the weight of Christ the Redeemer (statue), and the weight of Christ the Redeemer (statue) is 1.08 times that amount.
(a.k.a. O Cristo Redentor, a.k.a. Christo redemptor) (Rio de Janeiro, Brazil)
Christ the Redeemer weighs 700 tons. 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 half as heavy as a Tree (Sierra Redwood).
In other words, 646 tons is 0.45 times the weight of a Tree (Sierra Redwood), and the weight of a Tree (Sierra Redwood) is 2.2 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 1,400 tons. 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 2,100 tons.
It's about four times as heavy as a House.
In other words, 646 tons is 3.76 times the weight of a House, and the weight of a House is 0.266 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 172 tons, 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 0.507 tons.
It's about five-and-a-half times as heavy as a Blue Whale.
In other words, 646 tons is 5.61 times the weight of a Blue Whale, and the weight of a Blue Whale is 0.178 times that amount.
(Balaenoptera musculus)
Blue whales weigh between 115 tons. The largest mammal to have ever lived, blue whales feed almost exclusively on krill — tiny invertebrates weighing about 0.0000011 tons each.
It's about eight-and-a-half times as heavy as The Space Shuttle.
In other words, the weight of The Space Shuttle is 0.12 times 646 tons.
(for Endeavour, a.k.a. OV-105, a.k.a. Orbiter Vehicle-105) (empty weight, excluding main engines)
When empty, the space shuttle Endeavour weighs 78 tons. The shuttle's spacious cargo bay carried the Chandra X-ray Observatory into orbit in 1999 — a payload that weighed 22 tons.
It's about one-fifteenth as heavy as The Eiffel Tower.
In other words, the weight of The Eiffel Tower is 17.2 times 646 tons.
(a.k.a. La Tour Eiffel) (Paris, France) (total weight)
The Eiffel Tower weighs approximately 11,100 tons. Architected to be quickly assembled, the Tower contains only 7.5 cu. m (260 cu. ft) of solid material.
It's about one-twenty-fifth as heavy as The Brooklyn Bridge.
In other words, the weight of The Brooklyn Bridge is 22.73 times 646 tons.
(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.