1. **Problem Statement:** Find the Curved Surface Area (CSA), Total Surface Area (TSA), Lateral Surface Area (LSA), and Volume of a frustum of a cone with the following dimensions: - Smaller base radius $r_1 = 6$ cm - Larger base radius $r_2 = 13$ cm - Slant height $l = 6$ cm - Height $h = 8$ cm 2. **Formulas and Explanation:** - Curved Surface Area (CSA) of a frustum: $$\text{CSA} = \pi (r_1 + r_2) l$$ - Total Surface Area (TSA) includes the areas of both circular bases plus the curved surface: $$\text{TSA} = \pi r_1^2 + \pi r_2^2 + \text{CSA}$$ - Lateral Surface Area (LSA) is the same as CSA for a frustum: $$\text{LSA} = \text{CSA}$$ - Volume of a frustum: $$\text{Volume} = \frac{1}{3} \pi h (r_1^2 + r_2^2 + r_1 r_2)$$ 3. **Calculations:** - Calculate CSA: $$\text{CSA} = \pi (6 + 13) \times 6 = \pi \times 19 \times 6 = 114\pi$$ - Calculate TSA: $$\text{TSA} = \pi \times 6^2 + \pi \times 13^2 + 114\pi = 36\pi + 169\pi + 114\pi = 319\pi$$ - Calculate LSA: $$\text{LSA} = \text{CSA} = 114\pi$$ - Calculate Volume: $$\text{Volume} = \frac{1}{3} \pi \times 8 \times (6^2 + 13^2 + 6 \times 13) = \frac{8\pi}{3} (36 + 169 + 78) = \frac{8\pi}{3} \times 283 = \frac{2264\pi}{3}$$ 4. **Final Answers:** - Curved Surface Area (CSA) = $114\pi$ cm² - Total Surface Area (TSA) = $319\pi$ cm² - Lateral Surface Area (LSA) = $114\pi$ cm² - Volume = $\frac{2264\pi}{3}$ cm³