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How heavy is 6.70 tons?

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It's about 500 times as heavy as a Gold Bar.
In other words, 6.70 tons is 488.54166670 times the weight of a Gold Bar, and the weight of a Gold Bar is 0.002046908315 times that amount.
(London Good Delivery bar)
A "London Good Delivery" gold bar — the variety commonly held by Central Banks — should weigh 0.01371428571 tons. The largest gold bar ever produced was minted by Mitsubishi Materials Corporation (a sibling company of the auto manufacturer) in 2005 and weighed 0.27557782770 tons.
It's about 700 times as heavy as a Dachshund.
In other words, the weight of a Dachshund is 0.001 times 6.70 tons.
(a.k.a. "Wiener dog", a.k.a. Teckel, a.k.a. Dackel, a.k.a. "hot dog dog", a.k.a. "sausage dog", a.k.a. "doxie") (FCI standard; standard size)
The Fédération Cynologique Internationale (FCI) calls for dachshunds to weigh about 0.01 tons. Despite of their small size, a 2008 survey conducted by the University of Pennsylvania named dachshunds as the most aggressive dog breed.
It's about 900 times as heavy as a Bowling Ball.
In other words, 6.70 tons is 893.3333330 times the weight of a Bowling Ball, and the weight of a Bowling Ball is 0.00111940299 times that amount.
(most common selection among male bowlers)
With an allowable range of 0.0055 tons, the most-preferred bowling ball weight among adult, male bowlers is 0.0075 tons. Because regulation balls measure the same diameter irrespective of their weight, ball density varies by size and balls weighing less than about 0.00551155655 tons will float in water.
It's about 1,000 times as heavy as a Gallon of Paint.
In other words, the weight of a Gallon of Paint is 0.001 times 6.70 tons.
(excluding container; average weight)
A gallon of paint weighs about 0.006 tons. Every day, 10,000,000 L (3,000,000 gal) of paint are applied in the United States.
It's about 1,000 times as heavy as a Cat.
In other words, the weight of a Cat is 0.001 times 6.70 tons.
(Felis catus) (Domestic; healthy weight)
The average domestic cat should weigh between 0.005 tons. Cats are known for their righting reflex, which allows them to land on their feet and survive falls from heights of 1 m (3 ft) up to about 21 m.
It's about one-one-thousand-five-hundredth as heavy as The Eiffel Tower.
In other words, 6.70 tons is 0.000602 times the weight of The Eiffel Tower, and the weight of The Eiffel Tower is 1,660 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 7.5 cu. m (260 cu. ft) of solid material.
It's about 2,000 times as heavy as a Brick.
In other words, 6.70 tons is 2,100 times the weight of a Brick, and the weight of a Brick is 0.00048 times that amount.
(Standard, traditional face brick - 1,900 cu. cm (120 cu. in))
A standard, traditional face brick weighs an average of 0.0032 tons. The steeple of the Church of St. Martin in Landshut, Germany is said to be the tallest brick tower in the world at a height of 130.6 m (428.5 ft) and was constructed using an estimated 650,000 bricks.