The dimensions of a box are x, 2x, and 3x. Each dimension is increased by 5. Calculate the volume of the box.

Question

The dimensions of a box are x, 2x, and 3x. Each dimension is increased by 5. Calculate the volume of the box.

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Gerda 3 months 2021-07-26T01:53:21+00:00 1 Answers 1 views 0

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    2021-07-26T01:55:11+00:00

    Answer:

    6x {}^{3}  + 55 {x}^{2}  + 150x + 125

    Step-by-step explanation:

    the volume of the box with given dimensions is :

    • x × 2x × 3x
    • 6x^3

    =》

    6 {x}^{3}

    the measures of sides after increase in each dimension by 5 are :

    1. x + 5
    2. 2x + 5
    3. 3x + 5

    so, volume =

    • (x+5) × (2x+5) × (3x+5)
    • (2x^2 + 5x + 10x + 25) × (3x+5)
    • (2x^2 + 15x + 25) × (3x+5)
    • 6x^3 + 10x^2 + 45x^2 + 75x + 75x + 125
    • 6x^3 + 55x^2 + 150x + 125

    volume of box after increase of 5 in each dimension is :

    6x {}^{3}  + 55 {x}^{2}  + 150x + 125

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