If anyone knows how to get the value of k, please show the steps.
$\displaystyle
V = 2\pi \int_0^1 {(x - k)\sqrt {{{(x + 4)}^2} - 16} dx} = 10{m^3}
$
Go to this website Wolfram|Alpha
In the input window, type in this exact expression: integrate (x-k)sqrt[(x+4)^2-16]dx (you can copy & paste)
Click the equals bar at the right-hand end of the input window.
Be sure you click ‘show steps’ to see the solution.