Question

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 circumference of the circular base of the cone and = 120°. Find:

a. the angle between [A F] and the base of the cone

Answer 1

The angle between [A_F] and the base of the cone = 68.2°

The area of the base of the cone ≈ 12.57 m²

Explanation:

The given parameters are;

The height of the cone = 5 m

The base radius of the cone = 2 m

The angle which the A
`\hat O`C = 120°

Therefore, we have;

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

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

∴ The angle between [A_F] and the base of the cone = The angle between [CF] and the base of the cone = 68.2°

The angle between [A_F] and the base of the cone = 68.2°

The area of the base of the cone = π × r² = π × 2² = 4·π ≈ 12.57

The area of the base of the cone ≈ 12.57 m².