### 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: Homework Help ✎

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(r2)/2.
The width of each cross-section is dx.

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