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
What is the area of a semicircle with diameter $10$?
Question 2
What is the area of an equilateral triangle with side length $6$?
Question 3
A solid has semicircular cross sections perpendicular to the $x$-axis. The diameter of each semicircle is $6$, and the base extends from $x=0$ to $x=4$. What is the volume of the solid?
Question 4
A solid has equilateral triangular cross sections perpendicular to the $x$-axis. The side length of each triangle is $8$, and the base extends from $x=0$ to $x=3$. What is the volume of the solid?
Question 5
The base of a solid is the region between $y=0$ and $y=x^2$ on the interval $[0,2]$. Cross sections perpendicular to the $x$-axis are semicircles whose diameters lie in the base region. What is the volume of the solid?