1. **Problem statement:** We have a large cone with radius $r=10$ cm and slant height $l=12$ cm. A smaller cone with radius $r=2$ cm and slant height $l=3$ cm is removed from the top, forming a frustum. We need to find: a) The curved surface area of the frustum in terms of $\pi$. b) The total surface area of the frustum in terms of $\pi$. 2. **Formula for curved surface area of a cone:** $$\text{Curved Surface Area} = \pi r l$$ where $r$ is the radius of the base and $l$ is the slant height. 3. **Step a) Curved surface area of the frustum:** The frustum is formed by removing the smaller cone from the larger cone. Curved surface area of frustum = Curved surface area of large cone $-$ Curved surface area of small cone. Calculate each: - Large cone curved surface area = $\pi \times 10 \times 12 = 120\pi$ - Small cone curved surface area = $\pi \times 2 \times 3 = 6\pi$ So, $$\text{Curved surface area of frustum} = 120\pi - 6\pi = 114\pi$$ 4. **Step b) Total surface area of the frustum:** Total surface area = Curved surface area + Area of two circular ends (top and bottom). - Bottom circle area = $\pi \times 10^2 = 100\pi$ - Top circle area = $\pi \times 2^2 = 4\pi$ Therefore, $$\text{Total surface area} = 114\pi + 100\pi + 4\pi = 218\pi$$ **Final answers:** - a) Curved surface area of frustum = $114\pi$ - b) Total surface area of frustum = $218\pi$