1. Problem statement: The height of a right prism is increased by 50%, while the base area remains the same. We need to find the percentage increase in the volume of the prism. 2. Let the original height be $h$ and the base area be $A$. The original volume $V$ is given by: $$V = A \times h$$ 3. The new height after a 50% increase is: $$h_{new} = h + 0.5h = 1.5h$$ 4. Since the base area remains the same, the new volume $V_{new}$ is: $$V_{new} = A \times h_{new} = A \times 1.5h = 1.5Ah$$ 5. The increase in volume is: $$\Delta V = V_{new} - V = 1.5Ah - Ah = 0.5Ah$$ 6. The percentage increase in volume is: $$\text{Percentage increase} = \frac{\Delta V}{V} \times 100 = \frac{0.5Ah}{Ah} \times 100 = 50\%$$ Final answer: The volume increases by 50%.