Volumes by disks

Answer Key - Grade 12 Math Worksheet - Challenge Me

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

1. 1.

   The region bounded by y = √x, y = 0 and x = 4 spins about the line x = 4. Ari uses horizontal disks. Write the volume as V = kπ. What is k?

   256/15
2. 2.

   The region bounded by y = √x, y = 0 and x = 9 spins about the line x = 9. Bo uses horizontal disks. Write the volume as V = kπ. What is k?

   648/5
3. 3.

   The region bounded by y = √x, y = 0 and x = 1 spins about the line x = 1. Esme uses horizontal disks. Write the volume as V = kπ. What is k?

   8/15
4. 4.

   The region bounded by y = √x, y = 0 and x = 16 spins about the line x = 16. Jun uses horizontal disks. Write the volume as V = kπ. What is k?

   8192/15
5. 5.

   Luz spins the region under y = eˣ, 0 ≤ x ≤ ln 3, about the x-axis. Write the volume as V = kπ. What is k?

   4
6. 6.

   Milo spins the region under y = eˣ, 0 ≤ x ≤ ln 5, about the x-axis. Write the volume as V = kπ. What is k?

   12
7. 7.

   Noah spins the region under y = eˣ, 0 ≤ x ≤ ln 6, about the x-axis. Write the volume as V = kπ. What is k?

   35/2
8. 8.

   Ren spins the region under y = sec x, 0 ≤ x ≤ π/3 about the x-axis. Write the volume as V = kπ. What is k? Give k to the nearest hundredth.

   1.73
9. 9.

   Tala spins the region under y = sin x, 0 ≤ x ≤ π about the x-axis. Write the volume as V = kπ. What is k? Give k to the nearest hundredth.

   1.57
10. 10.

    Zee spins the region under y = 2√(sin x), 0 ≤ x ≤ π/2 about the x-axis. Write the volume as V = kπ. What is k? Give k to the nearest hundredth.

    4