If the radius and height of a cone are each increased by $10\%$, then the volume of the cone is increased by:

The initial volume of a cone is given by:
$$V=\frac{1}{3}\pi r^{2}h$$

When both the radius ($r$) and height ($h$) increase by $10\%$, the new dimensions become:

$$r^{\prime }=1.1r$$

$$h^{\prime }=1.1h$$

The new volume ($V^{\prime }$) is:

$$V^{\prime }=\frac{1}{3}\pi (r^{\prime }{)}^2{h}^{\prime }=\frac{1}{3}\pi (1.1r{)}^2(1.1h)$$

$$V^{\prime }=\frac{1}{3}\pi (1.21r^2)(1.1h)=1.331\times \left(\frac{1}{3}\pi r^{2}h\right)=1.331V$$

The percentage increase in volume is:

$$\text{Percentage Increase}=(1.331-1)\times 100\%=33.1\%$$