Prism Volume Percentage Increase

The volume ($V$) of a prism is calculated by multiplying its base area ($A$) by its height ($H$). The formula is:

$ V = A \times H $

Analyzing the Changes

Let the initial base area be $A$ and the initial height be $H$. The initial volume is $V = A \times H$.

The base area is increased by 25%. The new base area, $A'$, is:

$ A' = A + 0.25A = 1.25A $

The height remains the same, so the new height $H'$ is:

$ H' = H $

Calculating New Volume and Percentage Increase

The new volume, $V'$, is:

$ V' = A' \times H' $

Substitute the expressions for $A'$ and $H'$:

$ V' = (1.25A) \times H $

$ V' = 1.25 \times (A \times H) $

Since $V = A \times H$, we have:

$ V' = 1.25V $

The increase in volume is:

$ \text{Increase} = V' - V = 1.25V - V = 0.25V $

To find the percentage increase in volume:

$ \text{Percentage Increase} = \frac{\text{Increase}}{\text{Original Volume}} \times 100\% $

$ \text{Percentage Increase} = \frac{0.25V}{V} \times 100\% $

$ \text{Percentage Increase} = 0.25 \times 100\% = 25\% $

Therefore, the volume increases by 25%.