
der Mantel
coat
A long item of clothing worn over normal clothes to protect oneself from cold or rain.
Zieh dir einen Mantel an, es ist kalt draußen!
Put on a coat; it's cold outside!
coat
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coat
A long item of clothing worn over normal clothes to protect oneself from cold or rain.
Zieh dir einen Mantel an, es ist kalt draußen!
Put on a coat; it's cold outside!

covering / layer
An outer covering, layer, or shell that covers or surrounds something.
Der Mantel des Fahrradreifens hat ein Loch.
The casing of the bicycle tire has a hole in it.

cloak of silence
An idiom meaning that a certain topic is deliberately not talked about in order to hide or ignore it.
Über den peinlichen Vorfall wurde schnell der Mantel des Schweigens gebreitet.
A cloak of silence was quickly spread over the embarrassing incident.
When 'Mantel' (coat) is an item of clothing, it is often used with the verbs 'anziehen' (to put on), 'ausziehen' (to take off), or 'tragen' (to wear).
Er zog seinen Mantel aus und hängte ihn an die Garderobe.
He took off his coat and hung it on the coat rack.
The meaning 'Hülle' (covering) or 'Schicht' (layer) can be recognized from the context. It is usually used for technical or scientific objects, such as 'Reifenmantel' (tire casing) or 'Erdmantel' (Earth's mantle).
Der äußere Mantel des Kabels schützt die inneren Drähte.
The outer covering of the cable protects the inner wires.
The expression 'den Mantel des Schweigens' (the cloak of silence) is usually combined with the verb 'breiten' (to spread) or 'hüllen' (to wrap). The thing being kept silent about is introduced with the preposition 'über' + accusative.
Über die wahren Gründe wurde der Mantel des Schweigens gebreitet.
A cloak of silence was spread over the real reasons.
jacket
A jacket and a coat are worn over other clothing and protect you from the weather. A coat, however, is long and covers more of the body. For a shorter outer garment, choose Jacke; for a long garment, choose Mantel.

Bei dem kühlen Wind zieht Lea einen langen Mantel an.
Lea puts on a long coat in the cool wind.
Bei dem kühlen Wind zieht Lea eine kurze Jacke an.
Lea puts on a short jacket in the cool wind.