A food company distributes its tomato soup in two cans of different sizes. For the larger can, the diameter has been increased by $30 \%$, and the height remains the same.
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.
Answer
Final Answer: The volume of the can increases by approximately \(\boxed{69\%}\).
Step 1 ：A food company distributes its tomato soup in two cans of different sizes. For the larger can, the diameter has been increased by $30 \%$, and the height remains the same.
Step 2 ：We are asked to find by what percentage does the volume of the can increase from the smaller can to the larger can.
Step 3 ：The volume of a cylinder (which is the shape of a can) is given by the formula \(V = \pi r^2 h\), where \(r\) is the radius and \(h\) is the height.
Step 4 ：Since the height remains the same, the increase in volume is due to the increase in the square of the radius.
Step 5 ：The radius is half of the diameter, so if the diameter increases by $30 \%$, the radius also increases by $30 \%$.
Step 6 ：Therefore, the volume increases by \((1+0.3)^2 - 1 = 0.69\) or $69 \%$.
Step 7 ：Final Answer: The volume of the can increases by approximately \(\boxed{69\%}\).
