
die Mulde
hollow
A shallow, usually gently sloping depression in the ground or in a surface.
Nach dem Regen sammelte sich das Wasser in einer Mulde auf der Wiese.
After the rain, water collected in a hollow in the meadow.
hollow / trough
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hollow
A shallow, usually gently sloping depression in the ground or in a surface.
Nach dem Regen sammelte sich das Wasser in einer Mulde auf der Wiese.
After the rain, water collected in a hollow in the meadow.

trough
A long, open container used, for example, as a feeding trough for animals or for mixing building materials such as mortar.
Der Maurer mischte den Zement in einer großen Mulde an.
The bricklayer mixed the cement in a large trough.
The preposition 'in' is used with the dative or accusative depending on the situation. 'In der Mulde' (in the hollow/trough; dative) describes a position, while 'in die Mulde' (into the hollow/trough; accusative) expresses movement toward it.
Das kleine Dorf liegt geschützt in einer Mulde.
The small village lies sheltered in a hollow.
In a geographical context, 'Mulde' (hollow) is often described with adjectives such as 'flach' (shallow), 'sanft' (gentle), or 'tief' (deep). Typical verbs are 'sich bilden' (to form) or 'sich befinden' (to be located).
Hinter dem Hügel befindet sich eine sanfte Mulde.
Behind the hill there is a gentle hollow.
You can recognize the meaning 'Behälter' (container) from words that point to the contents or use. These include, for example, 'Mörtel' (mortar), 'Zement' (cement), 'Futter' (feed), or verbs like 'mischen' (to mix) and 'füllen' (to fill).
Der Bauer füllte Futter in die Mulde für die Schweine.
The farmer filled the trough with feed for the pigs.
depression / deepening
Vertiefung and Mulde both refer to a place that lies lower than its surroundings. Vertiefung mainly says that the place is lower than the area around it. Mulde more specifically describes a shallow, usually gently sloping shape and is appropriate when this shape is important.

Auf der Metallplatte bildet eine flache Mulde eine Ablage für die Seife.
A shallow hollow in the metal plate serves as a place to set the soap.
Auf der Metallplatte ist eine kleine Vertiefung von einem Schlag geblieben.
A small depression caused by an impact remained on the metal plate.