From time to time, when grain storage is limited farmers will store grain in conical piles in their fields. Depending on how long the grain remains in these piles, the grain may be left uncovered or will be covered with a tarp. Wheat will form a conical pile with an angle of $25 ∘$ between the slant side and the horizontal (ground). This angle is called the angle of repose. The angle of repose varies from one kind of grain to another. Corn, for example, has an $22 ∘$ angle of repose. Suppose a conical pile of wheat is 3 m in height. What is the length of the slant side of the conical pile?

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6.856 m

7.2 m

7.098 m

6.8 m

answer is C.

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Detailed Solution

Let the diagram of the situation be,
Question Image

We have,

A O = 3 m

and

∠ A B O = 25 ∘

.
To find AB, we have

sin θ = P e r p e n d i c u l a r H y p o t e n u s e sin 25 ∘ = 3 A B 0.4226 = 3 A B A B = 3 0.4226 A B = 7.098 m

Hence, the correct option is 3.

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