• # question_answer The volume of the solid formed by rotating the area enclosed between the curve $y={{x}^{2}}$ and the line $y=1$ about $y=1$ is (in cubic units [UPSEAT 2003] A)            $9\pi /5$                              B)            $4\pi /3$ C)            $8\pi /3$                              D)            $7\pi /5$

Volume of the solid formed by rotating the area enclosed between the curve $y={{x}^{2}}$ and line $y=1$ will be $\int_{0}^{1}{2\pi \,xdy}$= $2\int_{0}^{1}{\pi \sqrt{y}dy}$= $\frac{4\pi }{3}[{{y}^{3/2}}]_{0}^{1}=\frac{4\pi }{3}$.