SOLUTION: A cylinder was altered by increasing the radius its circle base by 10 percent and decreasing its height by k percent. If the volume of the resulting cylinder is 8.9% greater than
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Question 1043633: A cylinder was altered by increasing the radius its circle base by 10 percent and decreasing its height by k percent. If the volume of the resulting cylinder is 8.9% greater than the volume of the original cylinder. what is the value of k?
A) 8.9
B) 10
C) 12
D) 15 Answer by Boreal(15235) (Show Source):
You can put this solution on YOUR website! Volume of original=pi*r^2h
Volume of new=pi*(1.1r)^2*(h-kh)
pi*1.21r^2*(h-kh)=1.089*pi^r^2*h
The pi cancels, the r^2 cancel
1.21(h-kh)=1.089h
1.21h-1.21kh=1.089h
0.121h=1.21kh
the h cancel
0.121=1.21k
k=0.121/1.21=0.10 or 10%
B
Let r=10 and h=20
volume of original is pi*100*20=2000pi
volume of new is pi*121*18=2178pi, which is 0.089 or 8.9% larger
