Let the original diameter of the canister be $d$, and let the original height of the canister be $h$. Then the original volume of the canister is $\pi r^2 h = \pi\left(\frac{d}{2}\right)^2 h$.
If the diameter of the canister is increased by 27%, then the new diameter is $1.27d$. Since the volume of the canister remains the same, we must have \[
\pi\left(\frac{1.27d}{2}\right)^2 h = \pi\left(\frac{d}{2}\right)^2 h,
\]from which \[
1.27^2 = \frac{d^2}{d^2}
\]and $d^2=1.27^2$. This means $d=1.27$. Thus the new height must be $\frac{d}{1.27}=\frac{1.27}{1.27}=\boxed{100}$ percent of the original height, which is a decrease of $\boxed{0}$ percent.
A company sells popcorn in cylindrical canisters. Marketing indicates that wider
canisters will increase sales. If the diameter of the canister is increased
by 27% while keeping the volume of the canister the same, by what
percent must the height be decreased? Express your answer to
the nearest whole number.
1 answer