jmc

Recall that increasing a quantity by $p\%$ is equivalent to multiplying it by $1+p\%$. If the original length, width, and height are $l$, $w$, and $h$, respectively, then the new length, width, and height are $1.1l$, $1.1w$, and $1.1h$. Therefore, the new volume is $(1.1l)(1.1w)(1.1h)=(1.1{)}^3(lwh)=1.331(lwh)$, which is 1.331 times greater than the original volume $lwh$. Multiplication by 1.331 corresponds to an increase of $33.1\%$, which to the nearest percent is $\boxed{33\%}$.

Note: The identity $$(1+x{)}^3=1+3x+3x^2+x^3$$ with the substitution $x=0.1$ may be used to quickly calculate $1.1^3$.