Question

Find the volume of the cone formed by the rotation round the x-axis of that part of the line 2x-y+1=0, intercepted between the axes...How?

Answer 1

\[2x-y+1=0\quad,\quad y=2x+1\quad;\quad A(-1/2,0)\quad,\quad B(0,1)\]1.\[r=1\quad,\quad h=1/2\quad\Rightarrow\quad V=\frac{\pi}{3}r^2h=\frac{\pi}{6}\]2.\[V=\pi\int\limits_{-1/2}^0(2x+1)^2dx=\pi\frac{(2x+1)^3}{6}|_{-1/2}^0=\pi\left(\frac{1}{6}-0\right)=\frac{\pi}{6}\]