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A certain barrel, which is a right circular cylinder, is filled to cap

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Bunuel
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A certain barrel, which is a right circular cylinder, is filled to cap [#permalink] New post   25 Jun 2015, 03:52
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A certain barrel, which is a right circular cylinder, is filled to capacity with 100 gallons of oil. The first barrel is poured into a second barrel, also a right circular cylinder, which is empty. The second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel. If all of the oil in the first barrel is poured into the second barrel, how much empty capacity, in gallons, is left in the second barrel?

A. There is no empty capacity
B. 100 gallons
C. 300 gallons
D. 700 gallons
E. 800 gallons

Source: McGraw-Hill

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D
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Re: A certain barrel, which is a right circular cylinder, is filled to cap [#permalink] New post   25 Jun 2015, 04:23
Formula : Volume of a cylinder = (22/7)*(r^2)*h

For original cylinder 1: Height = h, Diameter = d
Therefore, (22/7) * (d/2)^2 * h = 100. ---------------------- (1)

For new cylinder 2: Height = 2h, Diameter = 2d
Therefore capacity = (22/7) * d^2 * 2h
Substituting value from equation (1),
Capacity for cylinder 2 = 800 gallons.

Therefore, after filling 100 gallons, 700 gallons space will remain.
Hence D !!
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Re: A certain barrel, which is a right circular cylinder, is filled to cap [#permalink] New post   25 Jun 2015, 05:37
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Bunuel wrote:
A certain barrel, which is a right circular cylinder, is filled to capacity with 100 gallons of oil. The first barrel is poured into a second barrel, also a right circular cylinder, which is empty. The second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel. If all of the oil in the first barrel is poured into the second barrel, how much empty capacity, in gallons, is left in the second barrel?

A. There is no empty capacity
B. 100 gallons
C. 300 gallons
D. 700 gallons
E. 800 gallons

Source: McGraw-Hill

Kudos for a correct solution.


If the first barrel has a capacity of 100 gallons, then the second barrell has quadruple capacity because it is twice as high and twice as "broad" as the first barrell making it quadruple in volume (2*2).

Answer C.
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Re: A certain barrel, which is a right circular cylinder, is filled to cap [#permalink] New post   25 Jun 2015, 10:55
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Volume of cylinder = (2/3)pie r^2 *h =(2/3)*pie * d^2*h/4
For cylinder 1: h1=height , v1=volume, d1 = diameter
For cylinder 2: h2=height , v2=volume, d2 = diameter
From question its given that: d2 = 2*d1; h2=2*h1
Applying volume equation and entering above values in that and the dividing volume of cylinder 1 to volume of cylinder 2.
V1/v2 = (d1/d2)^2 *h1/h2
100/v2 = (1/4)*1/2 => v2 =800= volume of cylinder 2.
Hence empty space left in the cylinder = v2-v1 =800-100 =700

Hence answer is D
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Re: A certain barrel, which is a right circular cylinder, is filled to cap [#permalink] New post   25 Jun 2015, 10:56
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Bunuel wrote:
A certain barrel, which is a right circular cylinder, is filled to capacity with 100 gallons of oil. The first barrel is poured into a second barrel, also a right circular cylinder, which is empty. The second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel. If all of the oil in the first barrel is poured into the second barrel, how much empty capacity, in gallons, is left in the second barrel?

A. There is no empty capacity
B. 100 gallons
C. 300 gallons
D. 700 gallons
E. 800 gallons

Source: McGraw-Hill

Kudos for a correct solution.


Radius of first cylinder=r, diameter=2r, height=h
Radius of second cylinder=2r, diamter=2d and height=2h
Volume of first cylinder=pie (r^2)*h=100
Volume of second cylinder=pie(2r^2)2h
Put the value of pie (r^2)*h=100 in the second cylinder,volume= pie (r^2)*4*2=100*8=800 gallons
Empty capacity=700 gallons
Answer D
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Re: A certain barrel, which is a right circular cylinder, is filled to cap [#permalink] New post   25 Jun 2015, 11:29
lipsi18 wrote:
Volume of cylinder = (2/3)pie r^2 *h =(2/3)*pie * d^2*h/4
For cylinder 1: h1=height , v1=volume, d1 = diameter
For cylinder 2: h2=height , v2=volume, d2 = diameter
From question its given that: d2 = 2*d1; h2=2*h1
Applying volume equation and entering above values in that and the dividing volume of cylinder 1 to volume of cylinder 2.
V1/v2 = (d1/d2)^2 *h1/h2
100/v2 = (1/4)*1/2 => v2 =800= volume of cylinder 2.
Hence empty space left in the cylinder = v2-v1 =800-100 =700

Hence answer is D
Thanks


The volume of a cylinder is \(\pi*r^2*h\)
The volume of a cone is \(\frac{1}{3}*\pi*r^2*h\)

Don't mix it up. Well, at least you got it right - look at my answer :lol:
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Re: A certain barrel, which is a right circular cylinder, is filled to cap [#permalink] New post   26 Jun 2015, 05:58
Bunuel wrote:
A certain barrel, which is a right circular cylinder, is filled to capacity with 100 gallons of oil. The first barrel is poured into a second barrel, also a right circular cylinder, which is empty. The second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel. If all of the oil in the first barrel is poured into the second barrel, how much empty capacity, in gallons, is left in the second barrel?

A. There is no empty capacity
B. 100 gallons
C. 300 gallons
D. 700 gallons
E. 800 gallons

Source: McGraw-Hill

Kudos for a correct solution.


Cylinder 1 : V1 - Volume, R1 - Radius, H1 height
Cylinder 2 : V2 - Volume, R2 - Radius, H2 heigh

V1 = 100,
R2 = 2 R1
H2 = 2 H1

\frac{V1}{V2} = \frac{(\(R1^2[}{m] * H1)/ ([m]2R1^2\) / 2H1}

V2= 800
We poured 100 so remaining = 700

Option D
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Re: A certain barrel, which is a right circular cylinder, is filled to cap [#permalink] New post   26 Jun 2015, 07:16
Just remember that the volume of cylinder depends on square of radius(diameter) and height.
If radius is doubled, the volume is increased four times and if height is also doubled volume is increased 8 times.

If first barrel was filled with 100 litres, second barrel will be of 800 litres capacity and hence 700 liters will be empty.

D

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Re: A certain barrel, which is a right circular cylinder, is filled to cap [#permalink] New post   26 Jun 2015, 08:10
Bunuel wrote:
A certain barrel, which is a right circular cylinder, is filled to capacity with 100 gallons of oil. The first barrel is poured into a second barrel, also a right circular cylinder, which is empty. The second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel. If all of the oil in the first barrel is poured into the second barrel, how much empty capacity, in gallons, is left in the second barrel?

A. There is no empty capacity
B. 100 gallons
C. 300 gallons
D. 700 gallons
E. 800 gallons

Source: McGraw-Hill

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So in gerenal: if you double the sides of any given 3D object, the volume will be 8-times the old Volume?
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Re: A certain barrel, which is a right circular cylinder, is filled to cap [#permalink] New post   25 Apr 2016, 00:39
the second barrel is twice as tall as the first ---> 2
the second barrel has twice the diameter, thus twice the radius ---> 2^2
therefore, the volume of the second barrel should be 2*2^2 the volume of the first ---> 8*100
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Re: A certain barrel, which is a right circular cylinder, is filled to cap [#permalink] New post   25 May 2019, 19:33
Bunuel wrote:
A certain barrel, which is a right circular cylinder, is filled to capacity with 100 gallons of oil. The first barrel is poured into a second barrel, also a right circular cylinder, which is empty. The second barrel is twice as tall as the first barrel and has twice the diameter of the first barrel. If all of the oil in the first barrel is poured into the second barrel, how much empty capacity, in gallons, is left in the second barrel?

A. There is no empty capacity
B. 100 gallons
C. 300 gallons
D. 700 gallons
E. 800 gallons

Source: McGraw-Hill

Kudos for a correct solution.

Volume of oil= PI(r^2)h = 100

Total volume of new barrel= (PI)*(2r)^2*(2h)= 8PI(r^2)h= 800

Empty space= 800-100=700 D
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Re: A certain barrel, which is a right circular cylinder, is filled to cap [#permalink]
25 May 2019, 19:33
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