1. **State the problem:** We need to find the volume of a prism given its cross-sectional area and length. 2. **Formula:** The volume $V$ of a prism is calculated by multiplying the cross-sectional area $A$ by the length $L$: $$V = A \times L$$ 3. **Given values:** - Cross-sectional area $A = 21$ cm$^2$ - Length $L = 3$ cm 4. **Calculate the volume:** $$V = 21 \times 3$$ 5. **Perform the multiplication:** $$V = 63$$ 6. **Conclusion:** The volume of the prism is $63$ cm$^3$. This means the prism occupies a space of 63 cubic centimeters.