If errors of 1% each are made in the base radius and height of a cylinder, then the percentage error in its volume, is

3%

Let V be the volume of the cone of base radius r and height h.

Then,

$V=\pi r^2 h$

$\Rightarrow d V=d\left(\pi r^2 h\right)$

$\Rightarrow d V=\pi\left(h d r^2+r^2 d h\right)$

$\Rightarrow d V=\pi\left(2 r h d r+r^2 d h\right)$

$\Rightarrow \frac{d V}{V}=\frac{\pi\left(2 r h d r+r^2 d h\right)}{\pi r^2 h}$

$ \Rightarrow \frac{d V}{V}=\frac{2}{r} d r+\frac{d h}{h}$

$\Rightarrow \frac{d V}{V} \times 100=2 \frac{d r}{r} \times 100+\frac{d h}{h} \times 100$

$\Rightarrow \frac{\Delta V}{V} \times 100=2\left(\frac{\Delta r}{r} \times 100\right)+\left(\frac{\Delta h}{h} \times 100\right)=2 \times 1+1=3$