Bowlingkuglen ligger i kuglerenden.

Because Danish usually puts the definite article at the end of the noun instead of using a separate word like the.

• en bowlingkugle = a bowling ball
• bowlingkuglen = the bowling ball

So -en here means the.

For the same reason: it is also definite.

• en kuglerende = a ball return channel / gutter
• kuglerenden = the gutter / the ball channel

So the full sentence has two definite nouns:

• bowlingkuglen = the bowling ball
• kuglerenden = the gutter

In Danish, ligge is often used to describe where something is physically located, especially when it is lying or resting somewhere.

So:

• Bowlingkuglen ligger i kuglerenden = The bowling ball is lying / is in the gutter

Using er is not impossible in every context, but ligger sounds more natural when talking about the position of an object.

This is a very common difference from English, where is is used much more broadly.

Ligge is the infinitive, and ligger is the present tense.

• at ligge = to lie
• ligger = lies / is lying

So the sentence is in the present tense.

Yes. Danish very often forms compound nouns as one word.

• bowling
  • kugle → bowlingkugle
• bowlingkuglen = the bowling ball

This is completely normal in Danish. English often writes similar ideas as two words, but Danish usually combines them.

It is also a compound noun.

• kugle = ball
• rende = channel, gutter, trench

Together, kuglerende literally means something like ball channel. In context, it refers to the gutter/channel connected with the bowling lane.

Then the definite ending is added:

• kuglerende = a gutter / ball channel
• kuglerenden = the gutter / the ball channel

Because i means in, and Danish treats this as being inside or down in the channel/gutter.

• i = in
• på = on

So i kuglerenden means the ball is in the gutter, not on it.

Because Danish usually expresses definiteness with a suffix attached to the noun.

Compare:

• en kugle = a ball

• kuglen = the ball

• en rende = a gutter/channel
• renden = the gutter/channel

A separate definite word can appear in some other structures, especially with adjectives:

• den store kugle = the big ball

But in your sentence, there is no adjective, so the suffix alone is enough.

Yes. This is standard Danish word order for a simple statement:

• Bowlingkuglen = subject
• ligger = verb
• i kuglerenden = prepositional phrase showing location

So it follows the normal pattern:

subject + verb + place

Yes. That would mean The ball is in the gutter.

Using bowlingkuglen makes the meaning more specific: it is explicitly a bowling ball, not just any ball.

So:

• Kuglen ligger i kuglerenden = The ball is in the gutter
• Bowlingkuglen ligger i kuglerenden = The bowling ball is in the gutter

It is capitalized only because it is the first word of the sentence.

In Danish, common nouns are not normally capitalized the way they are in German.

So in the middle of a sentence, it would be:

• Jeg tror, bowlingkuglen ligger i kuglerenden.

not Bowlingkuglen.

The important thing is to hear them as compounds, not as random long strings.

Roughly:

• bowlingkuglen ≈ BOW-ling-koo-len
• kuglerenden ≈ KOO-le-ren-den

A few useful points:

• g in ligger is not pronounced like a hard English g
• the u in kugle is not exactly like English oo, though that rough approximation can help at first
• the stress usually falls early in the compound

You do not need perfect pronunciation immediately, but it helps to recognize where one part of the compound ends and the next begins.

Yes, the exact interpretation depends on context.

Literally, kuglerende means something like ball channel/gutter, so a learner may need context to know exactly which channel is meant. In a bowling setting, it could refer to the lane gutter or another channel associated with the ball.

So grammatically the sentence is clear, but the exact real-world reference can depend on the situation.

Both base nouns here are common gender nouns, which is why they take en in the indefinite singular and -en in the definite singular.

• en kugle → kuglen
• en rende → renden

In compounds, the gender usually comes from the final part of the compound. So:

• bowlingkugle ends with kugle, which is common gender
• kuglerende ends with rende, which is also common gender

That is why both definite forms end in -en.