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`

Step-by-step 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`