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# math

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A cylinder shaped container has a radius of 30 cm and a height of 100cm. A glass sphere with a radius of 12 cm is placed inside the cylinder shaped container and then the container is completely filled with water.

What is the approximate volume of the water contained in the cylinder?

Use 3.14 to approximate for π

Mar 1, 2019

#1
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I am editing this because Lagtho correctly pointed out I used a cone instead of a cylinder  !!

cone volume - sphere volume = water volume

CYLINDER volume - sphere volume = water volume

pi r^2 h  - 4/3 pi r^3 = water vol     (this assumes the water can squeeze past the sphere to fill the tip of the cone)

pi 30^2  100   - 4/3 pi 12^3 = water vol

= 275365  cm^3

Mar 1, 2019
edited by ElectricPavlov  Mar 1, 2019
#2
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This is good, but you used the formula for a cone, not a cylinder.

Cylinder - Sphere = Remaining volume.

Cylinder = pi r^2 * h = pi 900 * 100 = 90,000 pi

Sphere = (pi r^3 * 4)/3 = (pi 1728 * 4)/3 = 2304pi

Remaining volume = 87696 pi = 275,365.44 cm^3

Mar 1, 2019
edited by LagTho  Mar 1, 2019