### Home > APCALC > Chapter 12 > Lesson 12.1.5 > Problem12-58

12-58.

Calculate the volume of the solid formed by revolving the region bounded by the $y$‑axis, the graph of $f ( x ) = 4 \sqrt { x ^ { 3 / 2 } + 1 }$, and the line $y = 12$ about the $y$‑axis.

To determine the bounds of integration, solve:

$12=4\sqrt{x^{3/2}+1}$

Using shells:

$\int_0^?2\pi x(12-\sqrt{x^{3/2}+1})dx$