### Home > APCALC > Chapter 11 > Lesson 11.3.1 > Problem11-89

11-89.

Multiple Choice: The base of a solid is the region between the curve $y = x \sin\left(x\right)$ and the $x$-axis on the interval $0 ≤ x ≤ π$. The cross-sections perpendicular to the $x$-axis are semicircles. The volume of the solid is:

1. $1.127$

1. $1.271$

1. $1.721$

1. $2.171$

1. $2.711$

The diameter of each semicircle is $y/2$.
The area of each semicircle is$π\left(r^{2}\right)/2$.
The width of each cross-section is $dx$.

$\int_0^\pi \frac{\pi (y/2)^2}{2}dx$