1. **State the problem:** Find the volume of a prism with base edges 7 cm and 10 cm, and a height $h$. 2. **Formula:** The volume $V$ of a prism is given by: $$V = \text{Base Area} \times \text{Height}$$ 3. **Calculate the base area:** Assuming the base is a rectangle with sides 7 cm and 10 cm, $$\text{Base Area} = 7 \times 10 = 70 \text{ cm}^2$$ 4. **Express volume in terms of height:** $$V = 70 \times h = 70h \text{ cm}^3$$ --- 5. **Second problem:** Given volume $V = 300$ dm³ and base area $A = 15$ in², find the height $h$. 6. **Formula:** $$V = A \times h$$ 7. **Solve for height:** $$h = \frac{V}{A}$$ 8. **Substitute values:** $$h = \frac{300}{15}$$ 9. **Simplify:** $$h = \cancel{\frac{300}{15}} = 20$$ 10. **Interpretation:** The height is 20 units (same units as volume divided by area units). --- **Final answers:** - Volume of prism: $$V = 70h \text{ cm}^3$$ - Height when volume is 300 dm³ and base area is 15 in²: $$h = 20$$