If percent increase in radius of cylinder is 300, then volume of the cylinder changes by how much percent? (Keeping height of the cylinder constant)

Let the initial radius of the cylinder be $r$ and the constant height be $h$.
The initial volume of the cylinder is given by:

$$V_1=\pi r^{2}h$$

The radius is increased by $300\%$. Therefore, the new radius $r^{\prime }$ becomes:

$$r^{\prime }=r+\frac{300}{100}r=r+3r=4r$$

The new volume $V_2$ with the updated radius is:

$$V_2=\pi (r^{\prime }{)}^{2}h=\pi (4r{)}^{2}h=16\pi r^{2}h$$

The change in volume ($\Delta V$) is:

$$\Delta V=V_2-V_1=16\pi r^{2}h-\pi r^{2}h=15\pi r^{2}h$$

To find the percentage change in volume:

$$\text{Percentage Change}=\left(\frac{\Delta V}{V_1}\right)\times 100=\left(\frac{15\pi r^{2}h}{\pi r^{2}h}\right)\times 100=15\times 100=1500\%$$

Thus, the volume changes by $1500\%$.