A heap of grain is shaped as a cone ADCF with height 5 m and base radius 2 m, as shown on the diagram. A and C are points on the

Answer:

The angle formed between [A_F] and the base of the cone measures 68.2°.

The surface area of the cone's base is approximately 12.57 m².

Step-by-step explanation:

The parameters given are;

Height of the cone = 5 m

Base radius of the cone = 2 m

The angle denoted as AC = 120°

Thus, we have;

The angle between [A_F] and the cone's base = The angle formed between [CF] and the base of the cone

The angle between [CF] and the cone's base = tan⁻¹(5/2) = tan⁻¹(2.5) ≈ 68.2°

Therefore, the angle between [A_F] and the base of the cone is 68.2°.

To find the area of the cone's base, we use π × r² = π × 2² = 4·π ≈ 12.57

The base area of the cone ≈ 12.57 m².