If cylinder A has three times the height and one-third

Question

If cylinder A has three times the height and one-third the diameter of cylinder B, what is the ratio of the volume of A to the volume of B?
A 3:1
B 1:1
C 1:3
D 1:9
E 1:27

Bunuel · Answer

Volume_A=\pi{r}^2*h ;
 Volume_B=\pi{(3r)}^2*\frac{h}{3}=3\pi{r}^2*h ;

Ratio 1:3.

Answer: C.

Shruti0805 · Answer

Hi  Bunuel ,

The question states that the height of cylinder A is 3 times the height of cylinder B and the diameter if A is  \frac{1}{3}  of cylinder B.
In the equation you've setup, I see that you've taken the radius of B as 3r and squared it. Is this a typo or am I misunderstanding the question.

Thanks in advance.

Bunuel · Answer

Cylinder A has three times the height of cylinder B, so if the height of A is h then the height of B is h/3;
Cylinder A has one-third the diameter of cylinder B, so if the diameter of A is d, then the diameter of B is 3d. The same ratio will be for the radius too: if the radius of A is r, then the radius of B is 3r.

As for the squaring: it's because the formula for the volume of a cylinder is  \pi{r}^2*h .

Hope it helps.

Abhishek009 · Answer

For Cylinder B -

Height = x
Radius = 3x

Volume_B = π*(3x)^2*x => 9x^3π

For Cylinder A -

Height = 3x
Radius = x

Volume_A = π*(x)^2*3x => 3x^3π

\frac{Volume_A}{Volume_B} = \frac{3x^3π}{9x^3π}

So,  \frac{Volume_A}{Volume_B} = 1:3

Thus, answer will be (C) 1 : 3

marcuccio · Answer

Pay attention Bunuel The question states that the cylinder A has 3 times the height and 1/3 the DIAMETER of cylinder B It means that 1/3 DIAMETER= 2/3 RADIUS !!!!! DIAMETER= 2*RADIUS :!:

Bunuel · Answer

The question implies that cylinder A has three times the height than the height of B and cylinder A has one-third the diameter than the diameter of B.

marcuccio · Answer

The question implies that cylinder A has three times the height than the height of B and cylinder A has one-third the diameter than the diameter of B.

What does it mean "one-third the diameter"???
It implies that 2/3 the radius.
Volume's formula use radius not diameter

Sent from my iPhone using  GMAT Club Forum mobile app

Bunuel · Answer

Dear marcuccio,

Cylinder A has one-third the diameter of cylinder B, so if the diameter of A is 2, then the diameter of B is 6 --> the radius of A is 1, then the radius of B is 3.

meganbailey · Answer

To solve by plugging in:

Cylinder A: 
H=3
D=2
V=1^2 x 3 x pi= 3pi

Cylinder B: 
H=1
D=6
V=3^2 X 1 x pi= 9pi

Compare: 3pi:9pi reduced is 1:3

shashankism · Answer

Let the radius and height of cylinder B be r and h respectively.
So, radius and height of cylinder A will be r/3 and 3h respectively.

Ratio of Volumes =  ({pi*{(\frac{r}{3})}^2*3h})/({pi*r^2*h}) 
= \frac{1}{3}

Archit3110 · Answer

let ha = 3
ra=1 ; da = 2
and hb=1
rb=3; db= 6
so ratio 
pi * 1*3/ pi * 9*1 = 1/3
IMO C

If cylinder A has three times the height and one-third

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If cylinder A has three times the height and one-third

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