1. **State the problem:** We have a solid cone with radius $r=5$ cm and perpendicular height $h=12$ cm. (i) Calculate the cost of painting the total surface area at a rate of 0.015 per cm². (ii) Calculate how many smaller cones with radius 1.25 cm and height 3 cm can be made by melting the original cone. 2. **Calculate the slant height $l$ of the original cone:** $$l=\sqrt{r^2 + h^2} = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \text{ cm}$$ 3. **Calculate the curved surface area (CSA) of the original cone:** $$\text{CSA} = \pi r l = \pi \times 5 \times 13 = 65\pi \text{ cm}^2$$ 4. **Calculate the base area of the original cone:** $$\text{Base area} = \pi r^2 = \pi \times 5^2 = 25\pi \text{ cm}^2$$ 5. **Calculate the total surface area (TSA) of the original cone:** $$\text{TSA} = \text{CSA} + \text{Base area} = 65\pi + 25\pi = 90\pi \text{ cm}^2$$ 6. **Calculate the cost of painting the total surface area:** $$\text{Cost} = 0.015 \times 90\pi = 1.35\pi \approx 4.24$$ 7. **Calculate the volume of the original cone:** $$V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi \times 5^2 \times 12 = \frac{1}{3} \pi \times 25 \times 12 = 100\pi \text{ cm}^3$$ 8. **Calculate the volume of one smaller cone:** $$V_s = \frac{1}{3} \pi r_s^2 h_s = \frac{1}{3} \pi \times 1.25^2 \times 3 = \frac{1}{3} \pi \times 1.5625 \times 3 = 1.5625\pi \text{ cm}^3$$ 9. **Calculate the number of smaller cones that can be made:** $$\text{Number} = \frac{\text{Volume of original cone}}{\text{Volume of smaller cone}} = \frac{100\pi}{1.5625\pi} = \frac{100}{1.5625} = 64$$ **Final answers:** (i) The cost of painting the cone is approximately 4.24. (ii) The number of smaller cones that can be made is 64.