Select the option that is closest in meaning (synonym) to the word sheath, which refers to a covering or protective layer around something.

Introduction / Context:
This vocabulary question asks for a synonym of the word sheath. In English, sheath most commonly refers to a case or covering for a blade or tool, or in biology and everyday usage, to a protective layer that surrounds something. The test taker needs to select the word which best captures this idea of an outer covering from among four options that describe very different concepts.

Given Data / Assumptions:

• Target word: sheath.
• Options: weapon, hide, encourage, coat.
• We are looking for a word that overlaps in meaning with covering or protective layer.
• We assume general English usage in both literal and figurative senses.

Concept / Approach:
A sheath is something that surrounds another object, usually to protect it. Common contexts include a knife sheath, a sheath around an electrical cable, or a protective sheath of tissue around a nerve. Among the options, coat can be used not only for clothing but also as a verb or noun referring to an outer layer covering a surface, such as a coat of paint or a thin coat of ice. Weapon, hide, and encourage do not have this core meaning of an outer protective covering. Thus, coat comes closest in sense to sheath.

Step-by-Step Solution:
Step 1: Recall the main meaning of sheath: a case or covering that encloses and protects something, often a blade or cable. Step 2: Examine option A, weapon, which refers to an instrument used to cause harm or defend, not a covering for such an instrument. Step 3: Examine option B, hide, which can mean animal skin or to keep something out of sight. Neither usage aligns closely with the idea of a structured protective case. Step 4: Examine option C, encourage, which is a verb meaning to give support, confidence, or hope, and has no relation to coverings. Step 5: Examine option D, coat, which as a noun can mean a layer of some substance that covers a surface and as a verb means to apply such a layer. Step 6: Recognise that a sheath and a coat both function as outer layers that protect or cover something. Step 7: Conclude that coat is the best available synonym for sheath in this list.

Verification / Alternative check:
In technical contexts, sheath is sometimes directly defined as a protective covering, for example, the sheath of an electrical cable or a sheath of myelin around a nerve. Similarly, coat is used in phrases like protective coat, coat of varnish, or coat of armour plating, all of which emphasise an external protective or insulating layer. While sheath and coat are not perfect synonyms in every context, coat is the only option among the given choices that shares this core idea of protective outer covering and can be considered a near synonym for exam purposes.

Why Other Options Are Wrong:
Weapon is wrong because it refers to an object used for attack or defense rather than something that covers another object. Hide is primarily animal skin or the act of concealing, which does not systematically convey the idea of a protective casing shaped for an object. Encourage is an abstract verb about emotional or motivational support and has no semantic connection to physical coverings. Therefore, none of these alternatives matches the meaning of sheath as well as coat does.

Common Pitfalls:
Students may be tempted by hide because animal skin can function as a cover, but the typical range of meaning for hide in dictionaries and usage does not focus on a designed protective casing. It is better seen as a source material than as a structured sheath. Another pitfall is to ignore context and overthink, but exam synonym questions usually target the primary, most common sense of the word. Remembering sheath as an outer protective case and relating it to coat as an outer layer helps avoid confusion.

Final Answer:
The word that is closest in meaning to sheath in this context is coat.