PencilGo

Grade 12 · Math · Calculus

12th grade Volumes by disks worksheet

6 printable versionsOn Level10 questions · answer keyFree · no account

Level: Building Confidence · On Level · Challenge Me

When it’s done, scan the sheet with your phone and PencilGo marks it and picks the next one. Create a free account

Version
Print

Volumes by disks

Grade 12 Math Worksheet

NameDate

Circle the best answer, or write your answer on the line.

  1. The region between y = x² (x ≥ 0), the y-axis and y = 4 spins about the y-axis. Ari uses horizontal disks. Write the volume as V = kπ. What is k?

  2. The region between y = x² (x ≥ 0), the y-axis and y = 9 spins about the y-axis. Bo uses horizontal disks. Write the volume as V = kπ. What is k?

  3. The region between y = x² (x ≥ 0), the y-axis and y = 1 spins about the y-axis. Esme uses horizontal disks. Write the volume as V = kπ. What is k?

  4. The region between y = x² and y = 4 spins about the line y = 4. Kira uses disks. Write the volume as V = kπ. What is k?

  5. The region between y = x² and y = 1 spins about the line y = 1. Luz uses disks. Write the volume as V = kπ. What is k?

  6. The region between y = x² and y = 9 spins about the line y = 9. Milo uses disks. Write the volume as V = kπ. What is k?

  7. Pia spins the region under y = √x, 0 ≤ x ≤ 25 about the x-axis. Which integral gives the volume?

    • π ∫ from 0 to 5 of x dx
    • π ∫ from 0 to 25 of x dx
    • π ∫ from 0 to 25 of √x dx
    • π ∫ from 0 to 25 of 2√x dx

  8. Ren spins the region under y = 2x, 0 ≤ x ≤ 5 about the x-axis. Which integral gives the volume?

    • π ∫ from 0 to 5 of 4x dx
    • π ∫ from 0 to 5 of 4x² dx
    • π ∫ from 0 to 10 of 4x² dx
    • π ∫ from 0 to 5 of 2x dx

  9. Tala spins the region under y = eˣ, 0 ≤ x ≤ 1/2 about the x-axis. Which integral gives the volume?

    • π ∫ from 0 to 1/2 of 2eˣ dx
    • π ∫ from 0 to 1/2 of e^(2x) dx
    • π ∫ from 1 to √e of e^(2x) dx
    • π ∫ from 0 to 1/2 of eˣ dx

  10. Zee spins the region under y = 1/x, 1 ≤ x ≤ 4 about the x-axis. Which integral gives the volume?

    • π ∫ from 1 to 4 of 1/x² dx
    • π ∫ from 1/4 to 1 of 1/x² dx
    • π ∫ from 1 to 4 of 2/x dx
    • π ∫ from 1 to 4 of 1/x dx
PencilGopencilgo.com

12th grade Volumes by disks worksheet – printable
Print: 123456

About this worksheet

Volumes by disks. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

  • I can find the volume of a solid of revolution by disks about the x- or y-axis.
  • I can find the radius when the spin line is y = c or x = c.
  • I can write the disk integral and use limits along the spin axis.

Standard: none (beyond CCSS)

Words to know

solid of revolution: The solid swept out when a region spins around a line.

disk: A thin coin-shaped slice of area πr².

radius: The distance from the spin line to the curve.

Common mistakes

Used the radius instead of its square. A disk's area is πr².

Squared twice the radius. The curve's height is the radius itself.

Used y as the radius of a horizontal disk; the radius is the x-distance, √y here.

Questions parents ask

What is the most common mistake with volumes by disks?

Used the radius instead of its square. A disk's area is πr².

Are these 12th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

More calculus

See all Calculus

Every sheet you scan goes into your child’s record: dated, marked and ready for the year-end portfolio. Homeschool records

Ready for easier practice?

Print a sheet, scan it when it’s done, and PencilGo picks the next one.

Create a free account