Calculus 2: Volumes of Solids of Revolution

The first-quadrant area is bounded by the curve $y^2 = 4x$, the x axis, and the line x = 4 is rotated about the y axis. Find the volume generated: (a) By the ring method (b) By the shell method

Use the shell method to determine the volume of the solid formed by rotating the region about the y axis.

$y = x^2 + 2$

$y = 0$, $x = 0$, $x = 2$

Use the shell method to determine the volume formed by the bounded region rotated about the x-axis.

$y = x^2$, $y = 0$, $x = 2$

Use the disk method to find the volume of the solid of rotation by rotating the bounded area around the y-axis

$y = 2x^2$, $y = 0$, $x = 2$

Determine the volume of the solid generated by rotating the function about the x-axis on $[0,3]$

$y = \sqrt{9 - x^2}$

Determine the volume of the solid generated by rotating the function about the y-axis on $[0,4]$

$y = \sqrt{x}$