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# For a certain cylinder, the diameter equals the height.

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For a certain cylinder, the diameter equals the height. [#permalink]

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24 Mar 2014, 16:20
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75% (hard)

Question Stats:

60% (02:12) correct 40% (01:40) wrong based on 194 sessions

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For a certain cylinder, the diameter equals the height. If every length in this cylinder is decreased by 60%, then to the nearest integer, by what percent does the volume decrease?

(A) 22%

(B) 40%

(C) 60%

(D) 84%

(E) 94 %

This is how I am doing it but getting the incorrect answer. Can someone please help?

Case 1: Assume diameter = 10 then radius = 5 and height will be 10

Volume = pi*r^2*h = 250pi ---------------------------------------------------------(1)

Decrease height by 60 %

New height = 4

New volume = pi*25*4 = 100pi-----------------------------------------------------(2)

Volume decrease in percent = Old - new / old *100

250 pi - 100 pi/250pi * 100 = 60 % which is not correct.
[Reveal] Spoiler: OA

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Re: For a certain cylinder, the diameter equals the height. [#permalink]

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24 Mar 2014, 19:47
3
KUDOS
Answer = E = 94%

Area of Cube = $$\pi r^2 h$$

Given that 2r = h

So the Area of cube = $$2 \pi r^3$$ ................. (1)

All dimension are decreased by 60%, so new dimension is $$\frac{40r}{100}= \frac{2r}{5}$$

Now the area of cube = $$2 \pi (\frac{2r}{5})^3$$

= $$2 \pi r^3 . (\frac{2}{5})^3$$ ......................... (2)

Reduction in the area = (1) - (2)

=$$2 \pi r^3 (1 - \frac{8}{125})$$

= $$2 \pi r^3 (\frac{117}{125})$$ ................ (3)

Comparing equation (1) & (3) ; finding the percentage reduction

= $$\frac{\frac{117}{125} . 2 \pi r^3 . 100}{2 \pi . r^3}$$

$$= 93.6 =\approx{94}$$

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For a certain cylinder, the diameter equals the height. [#permalink]

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24 Mar 2014, 20:00
1
KUDOS
enigma123 wrote:
For a certain cylinder, the diameter equals the height. If every length in this cylinder is decreased by 60%, then to the nearest integer, by what percent does the volume decrease?

(A) 22%

(B) 40%

(C) 60%

(D) 84%

(E) 94 %

This is how I am doing it but getting the incorrect answer. Can someone please help?

Case 1: Assume diameter = 10 then radius = 5 and height will be 10

Volume = pi*r^2*h = 250pi ---------------------------------------------------------(1)

Decrease height by 60 %

New height = 4

New volume = pi*25*4 = 100pi-----------------------------------------------------(2)

Volume decrease in percent = Old - new / old *100

250 pi - 100 pi/250pi * 100 = 60 % which is not correct.

In this case, the equation (2) is incorrect

Problem says "If every length in this cylinder is decreased by 60%"; means height & radius both are decreased by 60%

So the new volume would be $$2 . \pi . (\frac{40}{100})^3 . 5^3$$

New volume = $$16 \pi$$ ............... (2)

Reduction = $$250 \pi - 16 \pi = 234 \pi$$

Percentage reduction = $$234 * \frac{100}{250} = 93.6$$

$$\approx{94}$$
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Last edited by PareshGmat on 08 Aug 2014, 03:28, edited 1 time in total.
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Re: For a certain cylinder, the diameter equals the height. [#permalink]

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25 Mar 2014, 02:40
1
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Expert's post
enigma123 wrote:
For a certain cylinder, the diameter equals the height. If every length in this cylinder is decreased by 60%, then to the nearest integer, by what percent does the volume decrease?

(A) 22%
(B) 40%
(C) 60%
(D) 84%
(E) 94 %

[Reveal] Spoiler:
This is how I am doing it but getting the incorrect answer. Can someone please help?

Case 1: Assume diameter = 10 then radius = 5 and height will be 10

Volume = pi*r^2*h = 250pi ---------------------------------------------------------(1)

Decrease height by 60 %

New height = 4

New volume = pi*25*4 = 100pi-----------------------------------------------------(2)

Volume decrease in percent = Old - new / old *100

250 pi - 100 pi/250pi * 100 = 60 % which is not correct.

The area of the cylinder is $$\pi{r^2}h$$. Since given that the diameter equals the height, then 2r=h and the area becomes $$2\pi{r^3}$$.

Now, if we decrease r by 60% it becomes 0.4r and thus the new volume becomes $$0.4^3*(2\pi{r^3})=0.064*(2\pi{r^3})$$. Therefore the volume decreased by approximately 1-0.06=0.94=94%.

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Re: For a certain cylinder, the diameter equals the height. [#permalink]

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25 Mar 2014, 02:57
A shorter approach :

Such questions can be done without even using the full formula for the volume of cylinder.

We just need to consider the exponent of the variables in the formula <In this case '$$r$$' and '$$h$$'>

The exponent of '$$r$$' is $$2$$ and the exponent of '$$h$$' is $$1$$ in the formula.

And since both the quantities decrease by the same percentage, the '$$new r$$' is .4r and '$$new h$$' is .4h.

So the new volume will be = $$(.4r)^2 * (.4h)$$ <we can neglect \pi since \pi is there in both the cases - new volume as well as original volume>

New volume(V') = (.4)^3 * r^2 *h = .064 r^2 * h => V' = .064 V
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Re: For a certain cylinder, the diameter equals the height. [#permalink]

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18 Jan 2015, 04:02
after doing the calculations the volume decrease comes to 96.8 percent closet integer given is 94. hence E.
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Re: For a certain cylinder, the diameter equals the height. [#permalink]

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18 Jan 2015, 06:54
1
KUDOS
enigma123 wrote:
For a certain cylinder, the diameter equals the height. If every length in this cylinder is decreased by 60%, then to the nearest integer, by what percent does the volume decrease?

(A) 22%

(B) 40%

(C) 60%

(D) 84%

(E) 94 %

This is how I am doing it but getting the incorrect answer. Can someone please help?

Case 1: Assume diameter = 10 then radius = 5 and height will be 10

Volume = pi*r^2*h = 250pi ---------------------------------------------------------(1)

Decrease height by 60 %

New height = 4

New volume = pi*25*4 = 100pi-----------------------------------------------------(2)

Volume decrease in percent = Old - new / old *100

250 pi - 100 pi/250pi * 100 = 60 % which is not correct.

Given, all the lengths of the cylinder are reduced by 60%
Hence all the lengths are now 40% of actual!

Original Volume (V)= (pi)(r*r)(h)
New Volume (V1) = (pi)(0.4r*0.4r)(0.4h) = (0.064)(pi)(r*r)(h) = 0.064V
Thus new Volume is 6.4% of original Volume
This implies the volume has reduced by 93.6% which after rounding off becomes 94%

Hence (E)
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Re: For a certain cylinder, the diameter equals the height. [#permalink]

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18 Jan 2015, 13:43
1
KUDOS
Expert's post
Hi All,

Since this question does not include any specific dimensions for the cylinder, we can TEST VALUES.

We're told that the Diameter = Height

IF....
Diameter = Height = 10

Volume = pi(R^2)(H)
V = pi(5^2)(10)
V = 250pi

We're then told that both measurements are reduced by 60%...

Diameter = Height = 4

New Volume = pi(2^2)(4)
New Volume = 16pi

The question asks us for the approximate percentage change in the Volume, so we need the Percentage Change Formula:

(New - Old)/Old = (16 - 250)/250 = -234/250

From here, we don't really need to calculate; we can use the answer choices to our advantage and do "comparison" math instead...

10% of 250 = 25
234 is "16 away" from 250, so it's less than 10% away. As such, the percentage decrease in the volume of the cylinder is greater than 90%.

[Reveal] Spoiler:
E

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Re: For a certain cylinder, the diameter equals the height. [#permalink]

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16 Nov 2017, 05:59
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Re: For a certain cylinder, the diameter equals the height.   [#permalink] 16 Nov 2017, 05:59
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