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

Question

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.

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 .

NickHalden · Answer

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 !!

reto · Answer

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.

lipsi18 · Answer

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

KS15 · Answer

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

reto · Answer

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:

vishwaprakash · Answer

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  * H1)/ ( 2R1^2  / 2H1}

V2= 800
We poured 100 so remaining = 700

Option D

akashganga · Answer

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

DJ

reto · Answer

So in gerenal: if you double the sides of any given 3D object, the volume will be 8-times the old Volume?

evdo · Answer

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

LeoN88 · Answer

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

bumpbot · Answer

Automated notice from GMAT Club BumpBot:

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

This post was generated automatically.

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

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Problem Solving (PS) Questions

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

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards