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How big is 5.56805364610 quarts?

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It's about ten times as big as a Blood Donation.
In other words, the size of a Blood Donation is 0.10 times 5.56805364610 quarts.
(American Red Cross donation volume)
The typical donation amount when giving blood is about 0.50 quarts. Donated quantities of blood typically have a viable shelf life of about 42 days.
It's about sixteen times as big as a Baseball (packed).
In other words, 5.56805364610 quarts is 16.030362 times the size of a Baseball (packed), and the size of a Baseball (packed) is 0.062381623 times that amount.
(64% packing density) (MLB rules)
Per Major League Baseball rules, a baseball must measure between about 0.213169240 quarts and 0.231431360 quarts. A major league pitcher can throw a fastball at up to 150 kph (91 mph).
It's about thirty times as big as a Baseball.
In other words, 5.56805364610 quarts is 25.0474406 times the size of a Baseball, and the size of a Baseball is 0.03992423881 times that amount.
(MLB rules)
Per Major League Baseball rules, a baseball must measure between about 0.21316924350 quarts and 0.23143136350 quarts. A major league pitcher can throw a baseball at up to 150 kph (91 mph) in a fastball pitch.
It's about thirty times as big as a Tennis Ball.
In other words, 5.56805364610 quarts is 33.460 times the size of a Tennis Ball, and the size of a Tennis Ball is 0.02989 times that amount.
(ITF Standard; for Type 2 ball)
Per International Tennis Federation standard, regulation tennis balls must measure 6.54 cm to 6.86 cm in diameter, for a total volume of 0.16640 quarts. Competition balls are also tested for bounce height, with the standards requiring that a ball dropped from 254 cm must bounce back to a height of 135 cm to 147 cm.
It's about 45 times as big as a Puck (Hockey).
In other words, 5.56805364610 quarts is 45.490740750 times the size of a Puck (Hockey), and the size of a Puck (Hockey) is 0.02198249542 times that amount.
(Ice hockey)
standard ice hockey puck measures about 0.12239971380 quarts. Hockey pucks can be shot or passed at speeds of up to 160 kph (99 mph) during games.
It's about 75 times as big as an Egg (Chicken).
In other words, the size of an Egg (Chicken) is 0.013 times 5.56805364610 quarts.
(hen; USDA large size; uncooked)
A typical egg — of large size as defined by the United State Department of Agriculture — has a volume of 0.072 quarts. Each year, American farms produce 69,000,000,000 eggs.
It's about 85 times as big as a Golf Ball (packed).
In other words, 5.56805364610 quarts is 82.89129150 times the size of a Golf Ball (packed), and the size of a Golf Ball (packed) is 0.0120639935 times that amount.
(64% packing density) (per R&A-USGA Rules of Golf)
Dictated by the Rules of Golf (as approved by the United States Golf Association and the Rules Committee of the Royal and Ancient Golf Club of Saint Andrews), a golf ball must have a volume of at least 0.0429903031 quarts. Golf balls are not required to have the familiar dimpled pattern, but the design has been popular since its invention in 1905 because it reduces drag while increasing lift.