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

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(69443) (Show Source): You can put this solution on YOUR website!
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 = 256000pi/3 cc
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For the cylinder:

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

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