1. **Problem statement:** Calculate the percentage change in the volume of a prism with a square base of side length $a$ and height $h$ when 1) the height $h$ is increased by 20%, 2) the side length $a$ is increased by 20%, 3) both the side length $a$ and height $h$ are increased by 20%. 2. **Formula and rules:** The volume $V$ of the prism is given by: $$V = a^2 \cdot h$$ If a length $x$ is increased by 20%, the new length is: $$1.2 \cdot x$$ 3. **Step 1: Increase height $h$ by 20%** $$V_1 = a^2 \cdot (1.2 \cdot h) = 1.2 \cdot (a^2 \cdot h) = 1.2 \cdot V$$ The volume increases by 20%. 4. **Step 2: Increase side length $a$ by 20%** $$V_2 = (1.2 \cdot a)^2 \cdot h = 1.2^2 \cdot a^2 \cdot h = 1.44 \cdot V$$ The volume increases by 44%. 5. **Step 3: Increase both $a$ and $h$ by 20%** $$V_3 = (1.2 \cdot a)^2 \cdot (1.2 \cdot h) = 1.2^2 \cdot 1.2 \cdot a^2 \cdot h = 1.2^3 \cdot V = 1.728 \cdot V$$ The volume increases by 72.8%.