Maths-

General

Easy

Question

# The volume of a cube is calculated by multiplying length, width and height. What is the volume of the cube with side (3x+2)?

Hint:

- Volume of cube is given by (side)3.
- Volume of cube = (a)3
- Identity: (a + b)3 = (a)3 + 3ab (a + b) + (b)3

## The correct answer is: Hence, Volume of cube = 27x3 + 54x2 + 36x + 8 cubic units.

### Answer:

- Step by step explanation:

- Given:

Side of cube = (3x + 2)

- Step 1:
- Calculate the volume of cube:

Volume of cube = (a)^{3}

Volume of cube = (3x+2)^{3}

As,

(a + b)^{3} = (a)^{3 }+ 3ab (a + b) + (b)^{3}

Therefore,

Volume of cube = (3x)^{3} + 3(3x) (2) [3x + 2] + (2)^{3}

Volume of cube = 27x^{3} + 18x (3x + 2) + 8

Volume of cube = 27x^{3} + 54x^{2} + 36x + 8

- Final Answer:

Hence, Volume of cube = 27x^{3} + 54x^{2} + 36x + 8 cubic units.

- Given:

^{3}= (a)

^{3 }+ 3ab (a + b) + (b)

^{3}

Therefore,

Volume of cube = (3x)

^{3}+ 3(3x) (2) [3x + 2] + (2)

^{3}

Volume of cube = 27x

^{3}+ 18x (3x + 2) + 8

Volume of cube = 27x

^{3}+ 54x

^{2}+ 36x + 8

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