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

A solid has a base region on the interval $0\le x\le 3$. Cross sections perpendicular to the $x$-axis are rectangles with height equal to the base length and width equal to $2$ times the base length. If the base length is $f(x)=x$, what is the cross-sectional area function?

Question 2

Which integral gives the volume of a solid whose base is the region under $y=5-x$ on $0\le x\le 5$ and whose cross sections perpendicular to the $x$-axis are squares?

Question 3

A solid has square cross sections perpendicular to the $x$-axis. The side length of each square is the distance between $y=x$ and $y=0$. What is the volume from $x=1$ to $x=3$?

Question 4

A solid has rectangular cross sections perpendicular to the $x$-axis. Each rectangle has base length equal to the distance between $y=4$ and $y=x^2$ and height equal to $3$ times the base length. On $0\le x\le 2$, what is the area of each cross section?

Question 5

Which description best matches a volume problem using cross sections with squares?