Question

11. The figure shows a solid cylindrical stone pillar with a hemispherical top. The pillar has a diameter 40 cm. If the pillar has the same mass as a solid stone sphere of the same material of radius 40 cm, find the height of the pillar​

Answer 1

Answer: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(67918) (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+=+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