Problem
A food company distributes its tomato soup in two cans of different sizes. For the larger can, both the diameter and the height have been increased by $10 \%$. By what percentage does the volume of the can increase from the smaller can to the larger can? Round your answer to the nearest percent. Ф\% $\%$ 믐 $\sqrt{\square}$ ? $\times$ S
Solution
Step 1 ：The volume of a cylinder is given by the formula \(V = \pi r^2 h\), where \(r\) is the radius and \(h\) is the height.
Step 2 ：If both the diameter (and hence the radius) and the height are increased by 10%, the new volume will be \(V' = \pi (1.1r)^2 (1.1h) = 1.331 \pi r^2 h = 1.331 V\).
Step 3 ：This represents an increase of 33.1% in volume.
Step 4 ：Rounding to the nearest percent, the volume of the can increases by approximately \(\boxed{33\%}\).
