Question

Prove that if number is trippled, then its cube is 27 times the cubes of given number

Answer 1

$\huge{ \star{ \purple{Solution :-}}}{ \star}$



Let the number be x

Its cube will be (x)³ i.e. x³


If the number is tripled, the number becomes 3 × x i.e. 3x


Cube of above number = (3x)³

=> 3x × 3x × 3x

=> 27x³



$\therefore{}$ Cube of original number : Cube of the new number

Cube of original number = 1

Cube of new number = 27

=> 1 : 27


$\therefore{}$ The cube of the new number is 27 times the original number.



✔️ Hence, proved.

Answer 2

Let the number be ' a '.

It's cube = a * a * a
It's cube = a ^ 3

On trippling the number,

The number = 3 * a = 3a
Cube of this number = ( 3a ) ^ 3 = 27a ^ 3

Now let us find the ratio so that we may find the required answer,

Cube of number : Cube of new number
a ^ 3 : 27a ^ 3

Cancelling the common term i.e. a ^ 3,

1 : 27

Hence,

The cube of new number is 27 times the cube of the initial number.