Question

Increasing the radius of a cylinder by 6 units increases the volume by y cubic units. Increasing the altitude of the cylinders by 6 units also increases the volume by y cubic units. If the original altitude is 2, then the original radius is

• A. 2
• B. 4
• C. 6
• D. $6\pi$
• E. 8

Answer 1

Answer: (C)

6

Let the radius of the cylinder is r.

Height of cylinder = 2 units

Volume = $\pi r^{2}h=2\pi r^2[\because h=2]$

$⟹2\pi {(r+6)}^2=2\pi r^2+y⟹2\pi r^2+24\pi r+72\pi =2\pi r^2+y\therefore y=24\pi (r+3)⟹8\pi r^2=2\pi r^2+y\therefore y=6\pi r^2⟹6\pi r^2=24\pi (r+3)⟹r^2-4r-12=0\therefore r=6units$