Question

the surface area to each face of a cube is X2 + 4 x + 4 cm2. find, (i) the length of the cube (ii) volume of the cube​

Answer 1

Step-by-step explanation:

Given:-.

The surface area of face of a cube is

(X^2 + 4 X + 4) cm^2.

To find:-

Find

(i) the length of the cube

(ii) volume of the cube

Solution:-

Given that:

The surface area of face a cube

= (X^2 + 4 X + 4)cm^2

=> X^2+2X+2X+4

=> (X+2)+2(X+2)

=> (X+2)(X+2)

=>(X+2)^2 cm^2

The surface area of face a cube = (X+2)^2 cm^2

The surface area of a face of a cube = a^2 sq.units

Since each face is in the form of a square and the area of a square is equal to surface area of a face of the cube = a^2 sq.units,

Where a is the length of the face of the cube

=> a^2 = (X+2)^2 cm^2

=> a = (X+2) cm

Length of the side of the cube = (X+2) cm

Volume of a cube of the length of the side 'a' is

a^3 cubic units.

=> V = (X+2)^3 cm^3

It is in the form of (a+b)^3

Where, a= X and b= 2

We know that

(a+b)^3 = a^3+3a^2b+3ab^2+b^3

=> (X+2)^3

=> X^3+3(X^2)(2)+3(X)(2)^2+(2)^3

=> (X^3+6X^2+12X+8) cm^3

Answer:-

i) The length of the cube = (X+2) cm

ii) Volume of the cube = (X^3+6X^2+12X+8) cm^3

Used formulae:-

• The surface area of a face of a cube = a^2 sq.units
• Volume of a cube of the length of the side 'a' is a^3 cubic units.
• (a+b)^3 = a^3+3a^2b+3ab^2+b^3