Question

2. The surface area of each of the face of a cube is (x2 + 6x + 9) cmFind
(1) the length,
(II) the volume,
of the cube.


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Answer 1

Answer:

(i) Length of cube is (x + 3) units

(ii) Volume of cube is (x³ + 9x² + 27x + 27) unit³.

Step-by-step explanation:

(i) Each face of a cube is a square.

So, SA of square = area of square = a² where a is its side.

Thus, a² = x² + 6x + 9

Factorizing x² + 6x + 9,

=> x² + 6x + 9

=> x² + 3x + 3x + 9

=> x(x + 3) + 3(x + 3)

=> (x + 3)(x + 3) => (x + 3)²

As x² + 6x + 9 = (x + 3)² = a²

∴ a = √(x + 3)² => (x + 3) units is the length of square, and thus, the side of cube.

(ii) Volume of cube = a³ where a is its side

Now, a = (x + 3)

So, volume of cube = (x + 3)³

=> x³ + 3³ + 3(x)(3)(x + 3)          [Using (a + b)³ identity]

=> x³ + 27 + 9x(x + 3)

=> x³ + 27 + 9x² + 27x

=> (x³ + 9x² + 27x + 27) unit³ is the volume of this particular cube.