5. Applications of Integrals

Volumes Of Revolution — Quiz

Test your understanding of volumes of revolution with 5 practice questions.

Practice Questions

Question 1

What is the volume of the solid generated by rotating the region bounded by $y = 2 - x^2$ and $y = 0$ about the x-axis from $x = -1$ to $x = 1$ using the disk method?

Question 2

When using the washer method to find the volume of a solid generated by rotating the region between $y = 4 - x^2$ and $y = x^2$ from $x = 0$ to $x = 2$ about the x-axis, what is the correct integral expression?

Question 3

What is the volume of the solid generated by rotating the region bounded by $y = x^3$ and $y = 0$ from $x = 0$ to $x = 1$ about the y-axis using the cylindrical shell method?

Question 4

When rotating the region bounded by $y = x^2$ and $y = 4$ about the line $y = 4$, which method is most appropriate for calculating the volume?

Question 5

What is the volume of the solid formed by rotating the region bounded by $y = 2x$ and $y = 0$ from $x = 0$ to $x = 3$ about the y-axis using the cylindrical shell method?