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04 Feb 2018, 21:46
Kudos
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
85% (01:06) correct
15%
(01:12)
wrong
based on 62
sessions
History
Date
Time
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Not Attempted Yet
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
(A) 1:8
(B) 1:4
(C) 1:2
(D) 1
(E) 2:1
05 Feb 2018, 00:29
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Bunuel
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
(C) is our answer.
05 Feb 2018, 10:04
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Bunuel
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
Radius of P = 2
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?
\(\frac{16\pi}{32\pi}=\frac{1}{2}= 1:2\)
Answer C
