Let R be the radius of the base of the whole cone (bottom radius of the frustum) and r be the radius of the top of the frustum (radius of the small cone removed).

Here's the solution to the problem: Let R be the radius of the base of the whole cone (bottom radius of the frustum) and r be the radius of the top of the frustum (radius of the small cone removed). Let H be the height of the whole cone and h be the height of the small cone removed. The height of the frustum is h_f. From the problem statement: The bottom diameter is thrice the top diameter. 2R = 3(2r) R = 3r. The height of the frustum is h_f = 12 m. We know that h_f = H - h. So, H - h = 12. Using similar triangles formed by the cross-section of the cone: (R)/(H) = (r)/(h) Substitute R = 3r into the ratio: (3r)/(H) = (r)/(h) 3h = H Now we have a system of two equations: 1) H - h = 12 2) H = 3h Substitute (2) into (1): 3h - h = 12 2h = 12 h = 6 m Now find H: H = 3h = 3 × 6 = 18 m i) The height of the whole cone is: H = 18 m ii) Given that the volume of the whole cone is V = 39,600 cm^3. We need to use the height of the whole cone in cm: H = 18 m = 18 × 100 cm = 1800 cm. The formula for the volume of a cone is V = (1)/(3) R^2 H. We are given = (22)/(7). Substitute the known values into the volume formula: 39600 = (1)/(3) × (22)/(7) × R^2 × 1800 Simplify the equation: 39600 = (22 × 1800)/(3 × 7) × R^2 39600 = (22 × 600)/(7) × R^2 39600 = (13200)/(7) × R^2 Now, solve for R^2: R^2 = (39600 × 7)/(13200) R^2 = (396 × 7)/(132) R^2 = 3 × 7 R^2 = 21 Finally, find R by taking the square root: R = sqrt(21) Calculate the value and round to four significant figures: R ≈ 4.58257569... R ≈ 4.583 cm The radius of the whole cone, correct to four significant figures, is: R = 4.583 cm