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# If cylinder P has a height twice that of cylinder Q and a radius half

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Math Expert
Joined: 02 Sep 2009
Posts: 53069
If cylinder P has a height twice that of cylinder Q and a radius half  [#permalink]

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04 Feb 2018, 20:46
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Difficulty:

15% (low)

Question Stats:

87% (01:12) correct 13% (01:22) wrong based on 47 sessions

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If cylinder P has a height twice that of cylinder Q and a radius half that of cylinder Q, what is the ratio between the volume of cylinder P and the volume of cylinder Q ?

(A) 1:8

(B) 1:4

(C) 1:2

(D) 1

(E) 2:1

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Joined: 07 Dec 2017
Posts: 890
Re: If cylinder P has a height twice that of cylinder Q and a radius half  [#permalink]

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04 Feb 2018, 23:29
Bunuel wrote:
If cylinder P has a height twice that of cylinder Q and a radius half that of cylinder Q, what is the ratio between the volume of cylinder P and the volume of cylinder Q ?

(A) 1:8

(B) 1:4

(C) 1:2

(D) 1

(E) 2:1

There are two ways to approach this, we'll show both.

As the calculation looks straightforward, we'll just do it.
This is a Precise approach.

Writing H,R for P and h,r for Q we have H = 2h and 2R = r
Since volume is h*pi*r^2 then the volume of P is (2h)(pi)(r^2)/4 and that of Q is (h)(pi)(r^2)
Dividing the two gives 1:2, answer (C).

As the question asks for relations between sides and areas/volumes, we'll look for a Logical approach.

In a cylinder, the area is proportional to the height and proportional to twice the radius.
So, increasing the height by a factor of 2 would increase the volume by a factor of 2.
Decreasing the radius by a factor of 2 decreases the volume by a factor of 4.
Then the volume of P was muliplied by 2 and then divided by 4 relative to Q meaning that P:Q is 1:2
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If cylinder P has a height twice that of cylinder Q and a radius half  [#permalink]

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05 Feb 2018, 09:04
Bunuel wrote:
If cylinder P has a height twice that of cylinder Q and a radius half that of cylinder Q, what is the ratio between the volume of cylinder P and the volume of cylinder Q ?

(A) 1:8

(B) 1:4

(C) 1:2

(D) 1

(E) 2:1

Another approach: assign values.

Height of P = 4. Q's height is half that of P
Height of Q = 2

Radius of Q = 4. P's radius is half that of Q

Volume of P:
$$\pi r^2h =\pi(2^2)(4)= 16\pi$$

Volume of Q:
$$\pi r^2h = \pi(4^2)(2)= 32\pi$$

Ratio between volume of P and volume of Q?
$$\frac{16\pi}{32\pi}=\frac{1}{2}= 1:2$$

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If cylinder P has a height twice that of cylinder Q and a radius half   [#permalink] 05 Feb 2018, 09:04
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