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How heavy is 1,300 tonnes?

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It's about as heavy as a Tree (Sierra Redwood).
(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 two times as heavy as Christ the Redeemer (statue).
In other words, 1,300 tonnes is 2.05 times the weight of Christ the Redeemer (statue), and the weight of Christ the Redeemer (statue) is 0.4880 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 one-tenth as heavy as The Eiffel Tower.
In other words, 1,300 tonnes is 0.1290 times the weight of The Eiffel Tower, and the weight of The Eiffel Tower is 7.750 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 7.5 cu. m (260 cu. ft) of solid material.
It's about eight-and-a-half times as heavy as a House.
In other words, 1,300 tonnes is 8.330 times the weight of a House, and the weight of a House is 0.120 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 one-tenth as heavy as The Brooklyn Bridge.
In other words, 1,300 tonnes is 0.0976 times the weight of The Brooklyn Bridge, and the weight of The Brooklyn Bridge is 10.250 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 twelve-and-a-half times as heavy as a Blue Whale.
In other words, the weight of a Blue Whale is 0.0806 times 1,300 tonnes.
(Balaenoptera musculus)
Blue whales weigh between 105 tonnes. The largest mammal to have ever lived, blue whales feed almost exclusively on krill — tiny invertebrates weighing about 0.000001000 tonnes each.
It's about eighteen times as heavy as The Space Shuttle.
In other words, the weight of The Space Shuttle is 0.056 times 1,300 tonnes.
(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 71 tonnes. The shuttle's spacious cargo bay carried the Chandra X-ray Observatory into orbit in 1999 — a payload that weighed 20 tonnes.