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How heavy is 669.80 tons?

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It's about as heavy as Christ the Redeemer (statue)
In other words, 669.80 tons is 0.957 times the weight of Christ the Redeemer (statue), and the weight of Christ the Redeemer (statue) is 1.0 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, 669.80 tons is 0.47 times the weight of a Tree (Sierra Redwood), and the weight of a Tree (Sierra Redwood) is 2.1 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, 669.80 tons is 3.9 times the weight of a House, and the weight of a House is 0.256 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 0.5070 tons.
It's about four-and-a-half times as heavy as The Statue of Liberty (without base)
In other words, 669.80 tons is 4.3 times the weight of The Statue of Liberty (without base), and the weight of The Statue of Liberty (without base) is 0.23 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 150 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 six times as heavy as a Blue Whale
In other words, 669.80 tons is 5.81 times the weight of a Blue Whale, and the weight of a Blue Whale is 0.172 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 0.00000110 tons each.
It's about eight-and-a-half times as heavy as The Space Shuttle
In other words, 669.80 tons is 8.6 times the weight of The Space Shuttle, and the weight of The Space Shuttle is 0.12 times that amount.
(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, 669.80 tons is 0.060 times the weight of The Eiffel Tower, and the weight of The Eiffel Tower is 16.6 times that amount.
(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 930 cu. meters of solid material.