Volumes by disks

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   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?

   81/2
2. 2.

   The region between y = x² (x ≥ 0), the y-axis and y = 16 spins about the y-axis. Jun uses horizontal disks. Write the volume as V = kπ. What is k?

   128
3. 3.

   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?

   512/15
4. 4.

   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?

   16/15
5. 5.

   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?

   1296/5
6. 6.

   The region between y = x² and y = 16 spins about the line y = 16. Noah uses disks. Write the volume as V = kπ. What is k?

   16384/15
7. 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. 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 2x dx
   • π ∫ from 0 to 5 of 4x dx
   • π ∫ from 0 to 10 of 4x² dx
   • π ∫ from 0 to 5 of 4x² dx
9. 9.

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

   • π ∫ from 1 to √e of e^(2x) dx
   • π ∫ from 0 to 1/2 of e^(2x) dx
   • π ∫ from 0 to 1/2 of eˣ dx
   • π ∫ from 0 to 1/2 of 2eˣ dx
10. 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/x dx
    • π ∫ from 1/4 to 1 of 1/x² dx
    • π ∫ from 1 to 4 of 1/x² dx
    • π ∫ from 1 to 4 of 2/x dx