Find the percentage change in the volume of a cylinder if the radius of the cylinder is decreased by 10%, while the height is increased by 33.33%.

We know that the volume of a cylinder with radius $$r$$ and height $$h$$ is $$\pi r^2h$$

Given that the radius of the cylinder is decreased by 10%, i.e. the new radius is $$r\left(1-\frac{10}{100}\right)=0.9r$$

Also, the height is increased by 33.33%, i.e. the new height is $$h\left(1+\frac{33.33}{100}\right)=\frac{4}{3}h$$

Hence, the new volume of the cylinder is $$\pi\left(0.9r\right)^2\frac{4}{3}h=1.08\pi r^2h$$

So, the percentage change is $$\frac{\left(1.08\pi r^2h-\pi r^2h\right)}{\pi r^2h}\times100=8\%$$

Hence, the answer is 8% increase.