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A cylindrical vessel of a certain height and radius can hold 30 liters

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Bunuel
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A cylindrical vessel of a certain height and radius can hold 30 liters [#permalink] New post   19 Aug 2015, 01:27
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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. 0%
B. 16.67%
C. 25%
D. 33.33%
E. 50%

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C
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Re: A cylindrical vessel of a certain height and radius can hold 30 liters [#permalink] New post   19 Aug 2015, 04:10
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Bunuel wrote:
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. 0%
B. 16.67%
C. 25%
D. 33.33%
E. 50%

Kudos for a correct solution.


Let R and H be the radius and height of the cylinder.

Let r be the radius of the sphere.

Volume of cylinder = Vc = \(\pi*R^2*H\) = 30---> As both radius and height of the cylinder are equal to the radius of the sphere ---> R=H=r --->\(\pi*r^3\) = 30

Additionally, volume of the sphere = Vs =\(\frac{4\pi*r^3}{3}\) = 4/3*30 = 40 l

Thus the % of sphere volume still empty = 10/40 = 25%. C is the correct answer.
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Re: A cylindrical vessel of a certain height and radius can hold 30 liters [#permalink] New post   17 Jul 2016, 02:49
Bunuel wrote:
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. 0%
B. 16.67%
C. 25%
D. 33.33%
E. 50%

Kudos for a correct solution.


Given Height of Cylinder=Radius of cylinder=Radius of Sphere
Given Volume of Cylinder=30 litre

Volume of cylinder = \(pi*r^2*h==>pi*r^3 (since\) \(r=h)==>pi*r^3\)
\(Pi*r^3=30 ...................Eq 1\)

Volume of sphere = \(\frac{4}{3}*Pi*r^3 ...................Eq 2\)
Put value of \(pi*r^3\) from Eq 1 to Eq 2
Volume of sphere = \(\frac{4}{3}*30=40\)
Now 30 litre water is poured inside the sphere. So it will have capacity of 10 as empty

\(\frac{Empty}{Total} =\frac{10}{40} =25\)%

ANSWER IS C
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Re: A cylindrical vessel of a certain height and radius can hold 30 liters [#permalink] New post   27 Sep 2020, 10:22
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Bunuel wrote:
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. 0%
B. 16.67%
C. 25%
D. 33.33%
E. 50%

Kudos for a correct solution.


You need to know the following volume formulas.

→ Cylinder: \(V = πr^2 · h\)

→ Sphere: \(V = \frac{4}{3} πr^3\)

The height and radius of the cylinder equals the radius of the sphere, so \(r = h\).

→ Cylinder: \(V = πr^3\)

→ Sphere: \(V = \frac{4}{3} πr^3\)

You actually don't need to use 30 liters in this problem. You would get the same answer no matter what this value was. When the water is transferred \(\frac{1}{3} πr^3\) will remain unfilled. Therefore, the proportion that is unfilled is

→ Unfilled: \(\frac{1}{3}πr^3 ÷ \frac{4}{3}πr^3 = \frac{1}{4}\).

Converting this to a percentage, you get (C) 25%.
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Re: A cylindrical vessel of a certain height and radius can hold 30 liters [#permalink] New post   27 Sep 2020, 11:06
As the height and radius of the cylindrical vessel is same as the radius of the sphere so r=h
Volume of cylinder thus is πr^3
Volume of sphere is 4/3πr^3
So πr^3 is 75% of the volume of the sphere.
As volume of cylinder / volume of sphere is 3/4 .
Converting to % = (3/4)*100 =75%
So % that is left empty is 100-75 =25%.
So, answer is C

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Re: A cylindrical vessel of a certain height and radius can hold 30 liters [#permalink]
27 Sep 2020, 11:06
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