Дочка попросила ещё кусочек торта, потому что ей понравились глазурь и посыпка.

Дочка is a more affectionate, everyday form of дочь (daughter).

• дочь = daughter
• дочка = daughter / little daughter / dear daughter

In many contexts, Russian uses diminutive forms much more naturally than English does. Here, дочка sounds warm and natural, especially in a family context. It does not always mean the daughter is literally very young, but it often gives that feeling.

Попросила is the past tense of попросить (to ask for / request), and it is in the feminine singular form.

Russian past tense agrees with gender and number:

• попросил = he asked
• попросила = she asked
• попросило = it asked
• попросили = they asked

Since дочка is feminine singular, the verb is попросила.

Here ещё means some more / another / an additional.

So:

• ещё кусочек торта = another small piece of cake / some more cake

Be careful: ещё can mean different things depending on context, such as still, yet, or more. In this sentence, it clearly means more.

Кусочек is a diminutive form of кусок (piece).

• кусок = piece
• кусочек = little piece / small piece

The diminutive makes it sound smaller, softer, and more natural in everyday speech. With food, Russian very often uses diminutives:

• кусочек торта = a little piece of cake

It can suggest either actual small size or just a friendly, natural tone.

Because after кусочек (a little piece), Russian normally uses the genitive case.

• торт = cake
• торта = of cake

So literally:

• кусочек торта = a little piece of cake

This is very common with words for portions, quantities, and containers:

• чашка чая = a cup of tea
• кусок хлеба = a piece of bread
• бутылка воды = a bottle of water

Russian uses нравиться / понравиться differently from English to like.

The structure is basically:

• Something is pleasing to someone

So:

• ей понравились глазурь и посыпка literally means
• the icing and sprinkles pleased her

That is why:

• ей is in the dative case = to her
• the thing liked becomes the grammatical subject

Also, понравиться is perfective, so it means came to like / liked as a completed reaction, not a general ongoing preference.

Ей is the dative form of она.

• она = she
• её / ее = her
• ей = to her

With нравиться / понравиться, the person who experiences the feeling goes in the dative:

• мне нравится = I like
• тебе нравится = you like
• ей понравилось = she liked it

So in this sentence, ей is required by the verb понравились.

Because the subject is глазурь и посыпка — two things joined by и (and).

Even though each noun is singular by itself:

• глазурь = icing
• посыпка = topping / sprinkles

Together they form a plural subject, so the verb is plural:

• понравились

Compare:

• Ей понравилась глазурь. = She liked the icing.
• Ей понравилась посыпка. = She liked the topping/sprinkles.
• Ей понравились глазурь и посыпка. = She liked the icing and the sprinkles.

Because the sentence is talking about those things as categories or components of the cake.

• глазурь is usually an uncountable noun, like icing or glaze
• посыпка can refer to the topping/sprinkle layer as a single element

So even though English might say sprinkles, Russian can use посыпка as a singular mass/collective noun meaning sprinkled topping. That is perfectly natural.

Посыпка is something sprinkled on top of food for decoration or flavor.

In a cake context, it often means:

• sprinkles
• decorative topping
• crumb topping, depending on context

Here the most natural English idea is probably sprinkles or topping. The exact translation depends on what kind of decoration is meant.

This is a perfective vs. imperfective difference.

• нравились = were pleasing / she liked them, focusing on an ongoing state or repeated feeling
• понравились = she liked them, focusing on the fact that she came to like them or reacted positively

In this sentence, понравились fits well because it explains why she asked for more cake: she tasted or saw the icing and sprinkles, liked them, and then asked for another piece.

Yes, Russian word order is flexible.

This sentence:

• Дочка попросила ещё кусочек торта, потому что ей понравились глазурь и посыпка.

is a very natural neutral order.

But other orders are also possible, for example:

• Потому что ей понравились глазурь и посыпка, дочка попросила ещё кусочек торта.

That version puts more emphasis on the reason first. Russian uses word order mainly for information structure, emphasis, and style, not as rigidly as English does.

Russian does not have articles like a/an and the.

So nouns appear without articles:

• дочка = the daughter / a daughter
• кусочек = a little piece / the little piece
• торта = of cake / of the cake

Whether the meaning is definite or indefinite is understood from context. In this sentence, English needs articles, but Russian does not.