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How heavy is 6.70 tons?

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It's about 15,000 times as heavy as a Football (American).
In other words, 6.70 tons is 14,786.206896550 times the weight of a Football (American), and the weight of a Football (American) is 0.000067630597014930 times that amount.
(a.k.a. "pigskin") (NFL standard)
Per National Football League official rules, an American football must weigh between 0.0004375 tons and 0.00046875 tons. Because of NFL regulations, ceremonial considerations, and backup requirements, each NFL Superbowl requires the manufacture of 144 balls exclusively for the event.
It's about 15,000 times as heavy as a Can of Soup.
In other words, the weight of a Can of Soup is 0.0000590 times 6.70 tons.
(for Campbell''s Condensed Tomato Soup, 317.9 ml)
A can of Campbell''s Tomato Soup weighs 0.00039 tons. Cans have been used to store soup and other foods since their invention in 1913, but a dedicated can opener was not developed until cans began to use thinner materials — prior to that time, cans were usually opened using various blunt instruments and tools.
It's about one-twenty-thousandth as heavy as The CN Tower.
In other words, 6.70 tons is 0.0000515490 times the weight of The CN Tower, and the weight of The CN Tower is 19,399 times that amount.
(a.k.a. La Tour CN, a.k.a. Canadian National Tower, a.k.a. Canada's National Tower) (Toronto, Canada)
The CN Tower weighs approximately 129,970 tons. The Tower is home to the world's highest glass floor — a viewing area that allows visitors to look straight down 342 m (1,120 ft) to the ground below.
It's about 20,000 times as heavy as a Human Heart.
In other words, the weight of a Human Heart is 0.0000500 times 6.70 tons.
(human; adult)
The average human heart weighs about 0.00034 tons. Each minute, the heart pumps between 10 and 20 liters (3 to 5 gallons) of blood through its chambers.
It's about 30,000 times as heavy as a Hamster.
In other words, the weight of a Hamster is 0.0000300 times 6.70 tons.
(for Syrian hamster, a.k.a. golden hamster, a.k.a. Mesocricetus auratus; adult)
An adult Syrian hamster has a typical weight of about 0.0002 tons. Known for transporting food in the pouches of their cheeks so that they can bury it later, some hamsters can store up to 0.03 tons of food in their borrows.
It's about one-thirty-five-thousandth as heavy as The Sears Tower.
In other words, 6.70 tons is 0.000030120 times the weight of The Sears Tower, and the weight of The Sears Tower is 33,200 times that amount.
(officially "Willis Tower" as of 2009) (Chicago, Illinois)
The Willis Tower weighs approximately 222,400 tons. The outer wall surface of the Tower is covered with black anodized aluminum panels which would total 110,000 sq. m (28 acres) if laid out together.
It's about 35,000 times as heavy as a Billiard Ball.
In other words, 6.70 tons is 37,286.9565217390 times the weight of a Billiard Ball, and the weight of a Billiard Ball is 0.0000268190298507460 times that amount.
(American-style, WPA specifications)
Per the World Pool-Billiard Association, a billiard ball weight must weigh between 0.000171875 tons and 0.0001875 tons. According to legend, the difficulty in obtaining elephant ivory for the manufacture of billiard balls in the 19th century inspired the search for a replacement material, which led to the development of the first industrial plastic.