Problem: Increasing the radius of a cylinder by 6 units increases the volume by y cubic units. Increasing the altitude of the cylinder by 6 units also increases the volume by y cubic units. If the original altitude is 2, then the original radius is:
Answer Choices:
A. 2
B. 4
C. 6
D. 6Ï€
E. 8
Solution:
V+y=π(r+6)2h=πr2(h+6);∴(r+6)2⋅2=r2⋅8
∴3r2−12r−36=0;∴r=6.