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)