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Last weeks POW and answer:
Fall is a beautiful time of year to take a hot air balloon ride! Hot air balloons fly by heating the air inside the “envelope” (an inner bag that is able to hold air) until it provides enough upward force to lift the basket and its occupants off the ground.
Billy’s new hot air balloon is 100 feet in diameter and looks like a basketball (it is a sphere). What volume of air, in cubic feet, will Billy’s hot air balloon hold when it is completely filled? Express your answer as a decimal to the nearest tenth.
ANSWER:
The formula for the volume of a sphere is (4/3)πr3 OR (2/3)πr2h
Since we know the diameter of the balloon is 100 feet and the radius (r) is ½ of the diameter, we know that the radius is 50 feet. If you use the second equation, then the height is equal to the diameter which means the height is 100 feet.
(4/3)π(50)3 ≈ 523,598.8 cubic feet (ft3)
(2/3)π(50)2(100) ≈ 523,598.8 cubic feet (ft3)
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