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
a. the angle between [A F] and the base of the cone
1 answer:
Answer:
The angle between [A_F] and the base of the cone = 68.2°
The area of the base of the cone ≈ 12.57 m²
Step-by-step explanation:
The given parameters are;
The height of the cone = 5 m
The base radius of the cone = 2 m
The angle which the AC = 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.
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Answer:
16 hours
Step-by-step explanation:
let t be time, n the number of computers and w the number of workers, then
t = ← k is the constant of variation
To find k use the condition n = 30, w = 6 and t = 10 , then
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60 = 30k ( divide both sides by 30 )
2 = k
t = ← equation of variation
When w = 5 and n = 40 , then
t = =
= 16 hours