1. **Problem Statement:** Calculate the volume of titanium needed for one triangular prism bead with a hole, then find the total titanium volume for 500 beads, the weight in pounds, the cost including taxes, and the selling price per bead for a $1.50 profit. 2. **Volume of Triangular Prism:** The volume formula is $$V = \text{Area of base} \times \text{length}$$. 3. **Area of Base (Triangle):** Given sides $a = 2$ cm, $c = 2$ cm, and height $h = 1.73$ cm, the base is $2$ cm. The area is $$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 \times 1.73 = 1.73 \text{ cm}^2$$. 4. **Volume of Prism:** Length $= 3$ cm, so volume without hole is $$V_{prism} = 1.73 \times 3 = 5.19 \text{ cm}^3$$. 5. **Volume of Hole (Cylinder):** Diameter $= 1$ cm, radius $r = 0.5$ cm, length $= 3$ cm. Volume of hole $$V_{hole} = \pi r^2 h = \pi \times 0.5^2 \times 3 = \pi \times 0.25 \times 3 = 0.75\pi \approx 2.3562 \text{ cm}^3$$. 6. **Net Volume of Titanium:** $$V_{titanium} = V_{prism} - V_{hole} = 5.19 - 2.3562 = 2.8338 \text{ cm}^3$$ (rounded to 4 decimals). 7. **Volume for 500 Beads:** $$500 \times 2.8338 = 1416.9 \text{ cm}^3$$. 8. **Weight of Titanium:** 1 cm³ weighs 0.01 pounds, so total weight $$= 1416.9 \times 0.01 = 14.169 \text{ pounds}$$. 9. **Cost of Titanium Before Tax:** $$14.169 \times 25.71 = 364.12$$. 10. **Cost After Taxes:** GST 5% and PST 7% total 12%, so $$\text{Total cost} = 364.12 \times (1 + 0.12) = 364.12 \times 1.12 = 407.81$$. 11. **Cost per Bead:** $$\frac{407.81}{500} = 0.8156$$. 12. **Selling Price per Bead:** To make $1.50 profit per bead, $$\text{Price} = 0.8156 + 1.50 = 2.3156 \approx 2.32$$. **Final answers:** - Titanium volume per bead: $2.8338$ cm³ - Titanium volume for 500 beads: $1416.9$ cm³ - Weight for 500 beads: $14.17$ pounds - Cost after taxes: $407.81$ - Selling price per bead: $2.32$