1. **State the problem:** Find the volume and surface area of a composite right prism made of two stacked rectangular prisms. 2. **Identify dimensions:** - Bottom prism: length $l_1=6$ cm, width $w_1=3$ cm, height $h_1=2$ cm. - Top prism: length $l_2=2$ cm, width $w_2=3$ cm, height $h_2=3$ cm. 3. **Volume formula for a rectangular prism:** $$V = l \times w \times h$$ 4. **Calculate volumes:** - Bottom prism volume: $$V_1 = 6 \times 3 \times 2 = 36 \text{ cm}^3$$ - Top prism volume: $$V_2 = 2 \times 3 \times 3 = 18 \text{ cm}^3$$ 5. **Total volume:** $$V = V_1 + V_2 = 36 + 18 = 54 \text{ cm}^3$$ 6. **Surface area formula for a rectangular prism:** $$SA = 2(lw + lh + wh)$$ 7. **Calculate surface areas individually:** - Bottom prism surface area: $$SA_1 = 2(6 \times 3 + 6 \times 2 + 3 \times 2) = 2(18 + 12 + 6) = 2(36) = 72 \text{ cm}^2$$ - Top prism surface area: $$SA_2 = 2(2 \times 3 + 2 \times 3 + 3 \times 3) = 2(6 + 6 + 9) = 2(21) = 42 \text{ cm}^2$$ 8. **Calculate the overlapping area between prisms:** The top prism sits on the bottom prism with base $2 \times 3$ cm, so the overlapping area is: $$A_{overlap} = 2 \times 3 = 6 \text{ cm}^2$$ 9. **Calculate total surface area:** The overlapping area is counted twice in the sum of individual surface areas, so subtract twice the overlapping base area: $$SA = SA_1 + SA_2 - 2 \times A_{overlap} = 72 + 42 - 2 \times 6 = 114 - 12 = 102 \text{ cm}^2$$ **Final answers:** - Volume: $54$ cm$^3$ - Surface area: $102$ cm$^2$