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Cylinder and a sphere

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Cylinder and a sphere

by cypherskull » Fri May 04, 2012 1:41 pm
A cylindrical vessel of a certain height and radius can hold 30 liters of water in it when filled to the brim. All the water in the cylindrical vessel is transferred to a spherical vessel. If the height and radius of the cylindrical vessel is the same as the radius of the spherical vessel, what percentage of the capacity of the spherical vessel will remain empty after the transfer?

A. 25%

B. 33.33%

C. 50%

D. 0%

E. 16.67%
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by tomada » Fri May 04, 2012 2:07 pm
I think the answer is (A).

The volume of a cylinder is expressed as Pi*(r^2)*h, such that r=radius of circular cylindrical base and h=height of cylinder.
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The volume of a sphere is expressed as (4/3)*Pi*(r^3), such that r=radius of sphere.

For both the height AND radius of the cylinder to equal the radius of the sphere, the height and radius of the cylinder must be equal to each other, or h=r.

Therefore, the volume of this particular cylinder = Pi*(r^2)*r = Pi*(r^3)

Since the volume of the sphere is (4/3)*Pi*(r^3), the volume of the sphere = (4/3)*(volume of cylinder)

Therefore, the sphere holds a volume of (4/3)*(30 liters of water) = 40 liters of water.
After moving all 30 liters of water from the cylinder to the sphere, the sphere can still hold another 10 liters of water, or 1/4 of its total capacity.
I'm really old, but I'll never be too old to become more educated.
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