Question

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

• A. $18\pi$
• B. $2\pi$
• C. $36\pi$
• D. $9\pi$

Answer 1

Answer: (D)

$9\pi$

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
$V=\left(\frac{\pi r^{2}h}{3}\right)$
$=\pi \left(\frac{B{O}^2\times AB}{3}\right)$
$=\pi \left(\frac{3^2\times 3}{3}\right)$
$=9\pi$.