Question

find volume of solid generated by revolving the region bounded by y = √(x) and the lines y = 2 and x = 0 about the x-axis

Answer 1

Let us find volume of solid generated by revolving the region bounded by $y = \sqrt x$ and the lines $y = 2$ and $x = 0$ about the $x$ -axis.

Let us sketch the graph of the region bounded by $y = \sqrt x$ and the lines $y = 2$ and $x = 0$:

$V=\pi\int\limits_0^4(2^2-(\sqrt x)^2)dx=\pi\int\limits_0^4(4- x)dx=\pi(4x-\frac{x^2}{2})|_0^4=\pi(16-\frac{16}{2})=8\pi$