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 of the can are increased by 30%, the new volume \(V'\) of the can will be \(V' = \pi (1.3r)^2 (1.3h) = 1.3^3 \pi r^2 h = 1.3^3 V\).
Step 3 :The percentage increase in volume is then given by \(\frac{V' - V}{V} \times 100\% = (1.3^3 - 1) \times 100\%\).
Step 4 :Calculating the above expression gives a percentage increase of approximately 119.7%.
Step 5 :Rounding to the nearest percent gives a final answer of 120%.
Step 6 :Final Answer: The volume of the can increases by approximately \(\boxed{120\%}\).