5. Applications of the Definite Integral

Volumes By Slicing — Quiz

Test your understanding of volumes by slicing with 5 practice questions.

Practice Questions

Question 1

Which formula gives the volume of a solid when the cross-sectional area perpendicular to the $x$-axis is $A(x)$ on the interval $[a,b]$?

Question 2

In the slicing method, what does the quantity $\Delta x$ usually represent?

Question 3

A solid has constant cross-sectional area $A(x)=5$ square units from $x=0$ to $x=3$. What is its volume?

Question 4

Cross-sections perpendicular to the $x$-axis are squares whose side length is $4-x$ on the interval $0\le x\le 4$. What is the volume?

Question 5

If the cross-sectional area is measured in square centimeters and the slicing interval is measured in centimeters, what unit does the volume have?