इस केक का आकार बड़ा है।

Because इस is the oblique form of यह.

In Hindi, यह becomes इस when it is followed by a postposition, or when it is part of certain noun phrases like this one:

• यह केक = this cake
• इस केक का = of this cake

So in इस केक का आकार, इस is the correct form before the rest of the phrase.

का shows a relationship like of or 's in English.

So:

• इस keक का आकार = the shape/size of this cake
• literally: this cake's shape/size

A very common Hindi pattern is:

• X का Y = Y of X / X's Y

For example:

• राम का घर = Ram's house
• किताब का रंग = the color of the book

Here, का connects केक and आकार.

Because का / की / के agrees with the noun that comes after it, not the possessor.

In इस केक का आकार:

• possessor: इस केक = this cake
• thing possessed: आकार = shape/size

Since आकार is masculine singular, Hindi uses का.

Compare:

• इस केक का आकार = the cake's size
  (आकार = masculine singular)
• इस केक की खुशबू = the cake's smell/aroma
  (खुशबू = feminine singular)
• इस केक के रंग = the cake's colors
  (रंग = masculine plural here)

आकार usually means shape, form, or size, depending on context.

In this sentence, it most naturally means something like size or overall shape/form.

So the sentence is not exactly the same as:

• यह केक बड़ा है = This cake is big

Instead, it is more specifically:

• इस केक का आकार बड़ा है = This cake's size is big / The cake is large in size

That sounds a bit more formal or descriptive.

Because बड़ा agrees with आकार, which is masculine singular.

In this sentence:

• आकार = masculine singular
• so the adjective is बड़ा
• and the verb is है

Compare the agreement:

• आकार बड़ा है = The size is big
  (आकार masculine singular)
• रोटी बड़ी है = The bread is big
  (रोटी feminine singular)
• सेब बड़े हैं = The apples are big
  (masculine plural)

So बड़ा is not agreeing with केक here in the main clause; it is agreeing with आकार.

Because here बड़ा is a predicate adjective, not a directly attached adjective.

Hindi has two common patterns:

1. Adjective before noun

   • बड़ा केक = a big cake

2. Noun + adjective + है

   • केक बड़ा है = The cake is big
   • आकार बड़ा है = The size is big

In your sentence, बड़ा is describing आकार as part of the statement, so it comes after the noun:

• आकार बड़ा है

है is the present-tense form of to be for singular subjects.

So:

• आकार बड़ा है = The size is big

Hindi often uses है where English uses is:

• वह खुश है = He/She is happy
• घर बड़ा है = The house is big

In casual speech, people sometimes drop है, but in standard written Hindi it is normally included.

A close literal breakdown is:

• इस = this (oblique form)
• केक = cake
• का = of / 's
• आकार = shape/size
• बड़ा = big/large
• है = is

So literally:

This cake's shape/size big is.

Natural English:

This cake is large in size
or
The size of this cake is large.

It is a borrowed word from English: cake → केक.

Hindi uses many loanwords, especially for modern or everyday items. Even when a word comes from English, it still behaves like a Hindi noun in sentences:

• यह केक = this cake
• केक का स्वाद = the taste of the cake
• केक बड़ा है = the cake is big

So although केक is borrowed, the grammar around it is fully Hindi.

Yes, but it means something slightly different.

• यह केक बड़ा है = This cake is big
• इस केक का आकार बड़ा है = This cake's size/shape is big

The second version is more explicit and a bit more formal or descriptive. It focuses on the cake's size/shape, not just the cake in general.

So both are possible, but they are not perfectly identical in emphasis.

A common transliteration is:

is kek ka aakaar baṛaa hai

You may also see:

is kek ka aakar bada hai

A rough pronunciation guide:

• इस = is
• केक = kek
• का = kaa
• आकार = aa-kaar
• बड़ा = ba-ṛaa
  The ड़ sound is a retroflex flap, something like a soft r/d sound.
• है = hai

Yes, it is grammatical and understandable, but it sounds a little formal or textbook-like.

In everyday conversation, people might more often say:

• यह केक बड़ा है। = This cake is big.
• इस केक का साइज़ बड़ा है। = This cake's size is big.

The sentence with आकार is perfectly correct, but साइज़ is also common in casual speech for size. आकार sounds a bit more standard or formal.