Step 1: Write the volume formula for a hemisphere

The volume ($V$) of a hemisphere in terms of its radius ($r$) is given by the formula: $V = \frac{2}{3} \pi r^3$

$V = \frac{2}{3} \pi r^3$

Step 2: Determine the new radius after a 50% increase

If the initial radius is $r$, an increase of $50\%$ makes the new radius ($r'$) equal to: $r' = r + 0.50r = 1.5r = \frac{3}{2}r$

$r' = 1.5r$

Step 3: Calculate the new volume ($V'$)

Substitute the new radius into the volume formula: $V' = \frac{2}{3} \pi (r')^3 = \frac{2}{3} \pi (1.5r)^3 = \frac{2}{3} \pi (3.375 r^3) = 3.375 V$

$V' = 3.375 V$

Step 4: Find the percentage increase in volume

The percentage increase is calculated as $\frac{V' - V}{V} \times 100\%$. Substituting $V' = 3.375 V$: $\text{Percentage Increase} = \frac{3.375 V - V}{V} \times 100\% = 2.375 \times 100\% = 237.5\% - 100\% = 125\%$ Wait, $3.375 - 1 = 2.375$, and $2.375$\times 100 = 2$