Problem Solving

REINE wrote:Geometry

We know that the area of a cylinder = pie*r^2*h; h = height, and r = radius

We have h = d = 2r;

Thus, r = h/2

Volume = pie*r^2*h = pie*(h/2)^2*h = (pie/4)*h^3

Since the height is decreased by 60%, the decreased height would be 40% of the initial height

h' = new height = 40% of h = 0.4h

Since Volume is proportional to h^3, the decreased volume would be (0.4)^3 times the initial volume.

(0.4)^3 = 0.064

The volume decreased by [(1 - 0.064)/1] *100% = (0.936)*100% = 93.6% = ~94% (Given that every length in this cylinder is decreased by 60%, then to the nearest integer)

The correct answer: E

Hope this helps!

Relevant book: Manhattan Review GMAT Geometry Guide

-Jay
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Hi REINE,

This question can be solved by TESTing VALUES.

We're told that the height and diameter of the cylinder are EQUAL, so let's TEST....

Height = 10, Diameter = 10

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

We're told to reduce each dimension by 60%, which would make the new dimensions...

Height = 4, Diameter = 4

and the new volume...

Volume = (pi)(R^2)(H) =
(pi)(2^2)(4) = 16pi

We're asked to determine the PERCENT CHANGE in Volume...

At this point, you can actually use the answer choices to your advantage and avoid the longer calculation (below). Since the original volume is 250pi, a 25pi decrease would equal a 10% decrease. The new volume is 16pi, which is LESS than 10% of the original volume - thus, the decrease in volume had to be MORE than 90%... and there's only one answer that matches. Here's the formal calculation though, if you'd like to see it:

Percent Change = (new - old)/(old) = (16pi - 250pi)/(250pi) = -234pi/250pi = -234/250 = -936/1000 = about a 94% decrease

Final Answer: E

GMAT assassins aren't born, they're made,
Rich