Question

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?

Answer 1

Answer:$5k^2+6k$

Explanation:

Given

initial side of cube is k cm

New dimensions are

k+2 cm

k+3 cm

k cm

$V_{initial}=k^3$

$V_{Final}=\left ( k+3\right )\left ( k+2\right )\left ( k\right )$

Now  $V_{final}-V{initial}=\left ( k+3\right )\left ( k+2\right )\left ( k\right )-k^3$

$\Delta V=k^3+5k^2+6k-k^3=5k^2+6k$