For a certain cylinder, the diameter equals the height.

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

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

\(= 93.6 =\approx{94}\)

Answer = E

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 = \(234 * \frac{100}{250} = 93.6\)

\(\approx{94}\)

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%.

Answer: E.
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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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after doing the calculations the volume decrease comes to 96.8 percent closet integer given is 94. hence E.

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)

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%.

Final Answer:

GMAT assassins aren't born, they're made,
Rich
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let h = 10 ; r= 5
vol ; 250 pi
60% decrease ; h= 4 and r= 2
vol; 16pi
% decrease ; 250pi-16pi/250pi =94%
IMO E

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