1) A cubic meter of helium gas can lift a load of one kilogram. Assume that the mass of the balloon (and string or ribbon) is negligible, and calculate the diameter of the spherical balloon required to lift:
A) a 21-gram mouse
B) a nine pound, two ounce newborn baby in a fifteen-pound car seat
C) a 230-pound giant panda (Ailuropoda melanoleuca)
D) a Humvee (5200 pounds)
Extra Credit 1: an average-sized rubber party balloon has approximately the same volume as a sphere eleven inches in diameter. Determine for each of the above how many such helium-filled balloons would be required to lift the object in question.
Extra Credit 2: a king-size waterbed mattress contains about 1.325 cubic meters of water when full. Determine for each of the above how many such helium-filled mattresses would be required to lift the object in question.
2) Annual world production of helium (mostly from natural gas) is 100 million cubic meters. How heavy of an object could this lift if it were all gathered together in a single spherical balloon?
1 cubic meter = 1000 liters
1 pound = 16 ounces
1 pound = 2.2046 kilograms
1 kilogram = 1000 grams
1 ounce = 28.35 grams
1 foot = 0.3048 meters
1 inch = 2.54 centimeters
1 foot = 12 inches
1 meter = 100 centimeters
volume of a sphere = (4π/3)r3, where r is the radius
diameter of a sphere = 2r, where r is the radius
π = 3.14159
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