Question

The volume generated by rotating the triangle with vertices at $(0,0),(3,0)$ and $(3,3)$ about axis is:

Answer 1

The given points form a isosceles right angled triangle with base of 3 units along x-axis and height of 3 units perpendicular to x axis.
If we rotate the triangle about its base BO, then we will get a cone centred at B, with base radius $r=BO=3$ units and height $h=AB=3$ units
Therefore the volume of the cone thus formed will be
$V=\frac{\pi r^{2}h}{3}$
$=\pi \left(\frac{B{O}^2\times AB}{3}\right)$
$=\pi \left(\frac{3^2\times 3}{3}\right)$
$=9\pi$.