8. Applications of Integration

Volumes With Cross Sections: Triangles And Semicircles — Quiz

Test your understanding of volumes with cross sections: triangles and semicircles with 5 practice questions.

Practice Questions

Question 1

The base of a solid is the region in the first quadrant bounded by $y=0$, $y=2x$, and $x=3$. Cross sections perpendicular to the $x$-axis are isosceles right triangles whose leg lies in the base region. What is the volume of the solid?

Question 2

The base of a solid is the region in the first quadrant bounded by $y=0$, $y=x$, and $x=4$. Cross sections perpendicular to the $x$-axis are semicircles whose diameters lie in the base region. What is the volume of the solid?

Question 3

What is the area of a semicircle with radius $r$?

Question 4

The base of a solid is the region in the first quadrant bounded by $y=0$, $y=4-x$, and $x=4$. Cross sections perpendicular to the $x$-axis are equilateral triangles with side length equal to the vertical distance in the base. What is the volume of the solid?

Question 5

A solid has semicircular cross sections perpendicular to the $x$-axis. Each semicircle has diameter $6$, and the base extends from $x=0$ to $x=2$. What is the volume of the solid?