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How heavy is 340.1 long tons?

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It's about half as heavy as Christ the Redeemer (statue).
In other words, 340.1 long tons is 0.544 times the weight of Christ the Redeemer (statue), and the weight of Christ the Redeemer (statue) is 1.84 times that amount.
(a.k.a. O Cristo Redentor, a.k.a. Christo redemptor) (Rio de Janeiro, Brazil)
Christ the Redeemer weighs 625 long 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 two times as heavy as a House.
In other words, 340.1 long tons is 2.22 times the weight of a House, and the weight of a House is 0.45 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 154 long 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 0.453 long tons.
It's about three-and-a-half times as heavy as a Blue Whale.
In other words, 340.1 long tons is 3.307 times the weight of a Blue Whale, and the weight of a Blue Whale is 0.3024 times that amount.
(Balaenoptera musculus)
Blue whales weigh between 102.8 long tons. The largest mammal to have ever lived, blue whales feed almost exclusively on krill — tiny invertebrates weighing about 0.0000009842 long tons each.
It's about one-fourth as heavy as a Tree (Sierra Redwood).
In other words, 340.1 long tons is 0.27 times the weight of a Tree (Sierra Redwood), and the weight of a Tree (Sierra Redwood) is 3.7 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 long 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 1,900 long tons.
It's about five times as heavy as The Space Shuttle.
In other words, 340.1 long tons is 4.9 times the weight of The Space Shuttle, and the weight of The Space Shuttle is 0.2 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 70 long tons. The shuttle's spacious cargo bay carried the Chandra X-ray Observatory into orbit in 1999 — a payload that weighed 19 long tons.
It's about one-thirtieth as heavy as The Eiffel Tower.
In other words, 340.1 long tons is 0.0342 times the weight of The Eiffel Tower, and the weight of The Eiffel Tower is 29.2 times that amount.
(a.k.a. La Tour Eiffel) (Paris, France) (total weight)
The Eiffel Tower weighs approximately 9,940 long tons. Architected to be quickly assembled, the Tower contains only 7.5 cu. m (260 cu. ft) of solid material.
It's about thirty times as heavy as an Anchor of a Cruise Ship.
In other words, 340.1 long tons is 30.6 times the weight of an Anchor of a Cruise Ship, and the weight of an Anchor of a Cruise Ship is 0.0327 times that amount.
(for QE2 forward anchor, a.k.a. RMS Queen Elizabeth 2)
Each of the forward anchors of the RMS Queen Elizabeth 2 weighs 11.1 long tons. The anchor of the QE2 now sits in front of the Holyrood Church in Southampton, England, United Kingdom, along a pedestrian tourist route known as "the QE2 mile."