Find the volume of the figure below;

Step 1: Identify the components and their dimensions. The figure is a composite shape consisting of a cylinder and a cone. For the cylinder: • Radius r = 7 cm • Height h_cyl = 10 cm For the cone: • Radius r = 7 cm (same as the cylinder's base) • Slant height l = 13 cm Step 2: Calculate the height of the cone. We use the Pythagorean theorem, where the radius, height, and slant height form a right-angled triangle: h_cone^2 + r^2 = l^2 h_cone^2 + (7 cm)^2 = (13 cm)^2 h_cone^2 + 49 cm^2 = 169 cm^2 h_cone^2 = 169 cm^2 - 49 cm^2 h_cone^2 = 120 cm^2 h_cone = sqrt(120) cm = 2sqrt(30) cm Step 3: Calculate the volume of the cylinder. The formula for the volume of a cylinder is V_cyl = r^2 h_cyl. V_cyl = (7 cm)^2 (10 cm) V_cyl = (49 cm^2) (10 cm) V_cyl = 490 cm^3 Step 4: Calculate the volume of the cone. The formula for the volume of a cone is V_cone = (1)/(3) r^2 h_cone. V_cone = (1)/(3) (7 cm)^2 (2sqrt(30) cm) V_cone = (1)/(3) (49 cm^2) (2sqrt(30) cm) V_cone = 98sqrt(30)3 cm^3 Step 5: Calculate the total volume of the figure. The total volume is the sum of the volume of the cylinder and the volume of the cone. V_total = V_cyl + V_cone V_total = 490 cm^3 + 98sqrt(30)3 cm^3 V_total = (490 + 98sqrt(30)3) cm^3 Now, we calculate the numerical value using ≈ 3.14159 and sqrt(30) ≈ 5.477225: V_total ≈ 3.14159 (490 + (98 × 5.477225)/(3)) cm^3 V_total ≈ 3.14159 (490 + (536.76805)/(3)) cm^3 V_total ≈ 3.14159 (490 + 178.92268) cm^3 V_total ≈ 3.14159 (668.92268) cm^3 V_total ≈ 2101.07 cm^3 The volume of the figure is approximately: 2101.07 cm^3 Send me the next one 📸