Question

Increasing the radius of the base of a cylinder by $6$ units increase 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 $2$ units, find the original radius ?

• A. $8$ units
• B. $4$ units
• C. $6$ units
• D. $5$ units

Answer 1

The correct option is C $6$ units

Volume of cylinder$=\pi r^{2}h$

Now, $2\pi {(r+6)}^2-2\pi r^2=y=\pi r^2(2+6)-2\pi r^2$

After expanding, $2\pi (12r+36)=6\pi r^2$

$\Rightarrow 4r+12=r^2\Rightarrow r^2-4r-12=0\Rightarrow (r-6)(r+2)=0$

So, $r=6$