8. Applications of Integration

Volumes With Cross Sections: Squares And Rectangles — Quiz

Test your understanding of volumes with cross sections: squares and rectangles with 5 practice questions.

Practice Questions

Question 1

For a solid with square cross sections perpendicular to the $x$-axis, and side length $s(x)$ on the interval $[a,b]$, which integral gives the volume?

Question 2

A base region is bounded by $y=2x$ and the $x$-axis from $x=0$ to $x=3$. Cross sections perpendicular to the $x$-axis are squares. What is the volume?

Question 3

A solid has rectangular cross sections perpendicular to the $x$-axis. If each rectangle has base length $w(x)$ and height $3w(x)$, what is the area of one cross section?

Question 4

The base of a solid is the region between $y=4-x^2$ and the $x$-axis on $[0,2]$. Cross sections perpendicular to the $x$-axis are squares. What integral gives the volume?

Question 5

The base of a solid is the region between $y=6$ and $y=x$ on $[0,4]$. Cross sections perpendicular to the $x$-axis are rectangles, and each rectangle has constant height $2$. What is the volume?