SOLUTION: A snowman built with three spheres made of packed snow. The top sphere has half the diameter of the middle sphere. The middle sphere has half the diameter of the bottom sphere. Th
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Question 335839: A snowman built with three spheres made of packed snow. The top sphere has half the diameter of the middle sphere. The middle sphere has half the diameter of the bottom sphere. The top sphere weighs 5 pounds. What is the total weight of the snowman?
a. 30 pounds
b. 65 pounds
c. 125 pounds
d. 250 pounds
e. 365 pounds Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! A snowman built with three spheres made of packed snow.
The top sphere has half the diameter of the middle sphere.
The middle sphere has half the diameter of the bottom sphere.
The top sphere weighs 5 pounds.
What is the total weight of the snowman?
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Let top sphere have diameter (2r) and radius = r:
Then top sphere has volume (4)(pi)(r)^3
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Middle sphere has diameter = (4r) and radius = 2r
Then middle sphere has volume (4)(pi)(2r)^3 = 8 times the volume of top sphere.
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Bottom sphere has d = (8r) and radius = 4r
Then bottom sphere has volume (4)(pi)(4r)^3 = 64 times the volume of top sphere.
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Note: middle sphere has 8 times the volume of top sphere so weighs 8*5=40 lbs.
bottom sphere has 64 times the volume of top sphere so weighs 64*5 = 320 lbs.
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Total weight = 365 lbs.
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Cheers,
Stan H.
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a. 30 pounds
b. 65 pounds
c. 125 pounds
d. 250 pounds
e. 365 pounds
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