Find the surface area of a cone whose base radius is 4 cm and the height is 10 cm. (Take pi = 3.142)

Here are the solutions to the problems. 2. Find the surface area of a cone whose base radius is 4 cm and the height is 10 cm. (Take = 3.142) Step 1: Identify the given values. Base radius r = 4 cm. Height h = 10 cm. = 3.142. Step 2: Calculate the slant height l. The slant height l of a cone is given by the formula l = sqrt(r^2 + h^2). l = sqrt(4^2 + 10^2) l = sqrt(16 + 100) l = sqrt(116) l ≈ 10.7703 cm Step 3: Calculate the total surface area of the cone. The total surface area A of a cone is given by the formula A = r l + r^2. A = (3.142 × 4 × 10.7703) + (3.142 × 4^2) A = (3.142 × 4 × 10.7703) + (3.142 × 16) A = 135.346016 + 50.272 A = 185.618016 cm^2 Step 4: Round the answer to one decimal place. A ≈ 185.6 cm^2 The surface area of the cone is 185.6 cm^2. 3. The base radius is 12 cm and the top radius is 5 cm. If the slant height is 14 cm, calculate the surface area of the frustum. (Take = 3.142) Step 1: Identify the given values. Base radius R = 12 cm. Top radius r = 5 cm. Slant height of frustum L = 14 cm. = 3.142. Step 2: Calculate the curved surface area of the frustum. The curved surface area of a frustum is given by the formula A_curved = (R+r)L. A_curved = 3.142 × (12+5) × 14 A_curved = 3.142 × 17 × 14 A_curved = 3.142 × 238 A_curved = 747.796 cm^2 Step 3: Calculate the area of the base. The area of the base is given by A_base = R^2. A_base = 3.142 × 12^2 A_base = 3.142 × 144 A_base = 452.448 cm^2 Step 4: Calculate the area of the top. The area of the top is given by A_top = r^2. A_top = 3.142 × 5^2 A_top = 3.142 × 25 A_top = 78.55 cm^2 Step 5: Calculate the total surface area of the frustum. The total surface area A_total of the frustum is the sum of the curved surface area, the base area, and the top area. A_total = A_curved + A_base + A_top A_total = 747.796 + 452.448 + 78.55 A_total = 1278.794 cm^2 The surface area of the frustum is 1278.794 cm^2. That's 2 down. 3 left today — send the next one.