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The volume generated when the region bounded by $ y=x,y=1,x=0$ is rotated about $y$-axis is

\[\begin{array}{1 1}(1)\frac{\pi}{4}&(2)\frac{\pi}{2}\\(3)\frac{\pi}{3}&(4)\frac{2\pi}{3}\end{array}\]

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Volume of cylinder with base radius 1 ad the height 1- volume of the cone with base radius 1 and height 1
$\qquad= \pi \times 1^2 \times 1 - \large\frac{1}{3} \pi \times 1^2 \times 1$
$\qquad= \large\frac{2}{3} $$\pi$
Hence 4 is the correct answer.
answered May 21, 2014 by meena.p

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