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A cubical box with edges of length k centimetres is to be enlarged so that the dimensions of the larger box are k + 2 centimetres, k + 3 centimetres, and k centimetres. The volume of the larger box is how many cubic centimetres greater than the volume of the original box?

Respuesta :

Answer:[tex]5k^2+6k[/tex]

Explanation:

Given

initial side of cube is k cm

New dimensions are

k+2 cm

k+3 cm

k cm

[tex]V_{initial}=k^3[/tex]

[tex]V_{Final}=\left ( k+3\right )\left ( k+2\right )\left ( k\right )[/tex]

Now  [tex]V_{final}-V{initial}=\left ( k+3\right )\left ( k+2\right )\left ( k\right )-k^3[/tex]

[tex]\Delta V=k^3+5k^2+6k-k^3=5k^2+6k[/tex]