1. **State the problem:** Calculate the volume of an L-shaped prism with given dimensions and express the answer in standard form to 2 significant figures. 2. **Identify the dimensions:** - Left vertical height: $9.8 \times 10^{6}$ cm - Bottom horizontal length: $1.3 \times 10^{7}$ cm - Right vertical height: $5.1 \times 10^{6}$ cm - Upper right horizontal length: $9.7 \times 10^{6}$ cm - Thickness (depth): $1.8 \times 10^{3}$ cm 3. **Approach:** The L-shaped prism can be divided into two rectangular prisms: - Prism A: height $9.8 \times 10^{6}$ cm, length $9.7 \times 10^{6}$ cm, depth $1.8 \times 10^{3}$ cm - Prism B: height $5.1 \times 10^{6}$ cm, length $(1.3 \times 10^{7} - 9.7 \times 10^{6})$ cm, depth $1.8 \times 10^{3}$ cm 4. **Calculate length of Prism B:** $$1.3 \times 10^{7} - 9.7 \times 10^{6} = (13 - 9.7) \times 10^{6} = 3.3 \times 10^{6} \text{ cm}$$ 5. **Calculate volume of Prism A:** $$V_A = \text{height} \times \text{length} \times \text{depth} = (9.8 \times 10^{6}) \times (9.7 \times 10^{6}) \times (1.8 \times 10^{3})$$ 6. **Calculate volume of Prism B:** $$V_B = (5.1 \times 10^{6}) \times (3.3 \times 10^{6}) \times (1.8 \times 10^{3})$$ 7. **Calculate $V_A$:** $$9.8 \times 9.7 = 95.06$$ $$95.06 \times 1.8 = 171.108$$ $$V_A = 171.108 \times 10^{6+6+3} = 171.108 \times 10^{15} = 1.71108 \times 10^{17} \text{ cm}^3$$ 8. **Calculate $V_B$:** $$5.1 \times 3.3 = 16.83$$ $$16.83 \times 1.8 = 30.294$$ $$V_B = 30.294 \times 10^{6+6+3} = 30.294 \times 10^{15} = 3.0294 \times 10^{16} \text{ cm}^3$$ 9. **Total volume:** $$V = V_A + V_B = 1.71108 \times 10^{17} + 3.0294 \times 10^{16} = (1.71108 + 0.30294) \times 10^{17} = 2.01402 \times 10^{17} \text{ cm}^3$$ 10. **Express in standard form to 2 significant figures:** $$V \approx 2.0 \times 10^{17} \text{ cm}^3$$ **Final answer:** The volume of the prism is approximately $2.0 \times 10^{17}$ cm$^3$.