SOLUTION: A solid cylindrical stone pillar has a top in the shape of a hemisphere. Given that the pillar is 40 cm in diameter and has the same mass as a solid stone sphere of the same materi

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Question 388010: A solid cylindrical stone pillar has a top in the shape of a hemisphere. Given that the pillar is 40 cm in diameter and has the same mass as a solid stone sphere of the same material, with radius 40 cm. Find the height of the pillar.
Answer by Alan3354(30983) About Me  (Show Source):
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A solid cylindrical stone pillar has a top in the shape of a hemisphere. Given that the pillar is 40 cm in diameter and has the same mass as a solid stone sphere of the same material, with radius 40 cm. Find the height of the pillar.
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The same material and the same weight --> same volume.
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The volume of the sphere =
V+=+4%2Api%2A40%5E3%2F3
V = 256000pi/3 cc
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For the cylinder:
V+=+pi%2Ar%5E2%2Ah+%2B+2%2Api%5Er%5E3%2F3
V+=+pi%2Ar%2A%28rh+%2B+2r%5E2%2F3%29+=+256000pi%2F3
pi*40*(40h + 2*1600/3) = 256000pi/3
1600h + 12800/3 = 256000/3
4800h = 12800 = 256000
48h = 2432
h = 50.333 cm for the cylindrical part
height overall = 50.333 + r = 90.333 cm