Volumes by washers

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 = 1 spins about the line x = −1. Ari uses horizontal washers. Write the volume as V = kπ. What is k?

   32/15
2. 2.

   The region bounded by y = √x, y = 0 and x = 4 spins about the line x = −1. Bo uses horizontal washers. Write the volume as V = kπ. What is k?

   544/15
3. 3.

   The region bounded by y = √x, y = 0 and x = 16 spins about the line x = −1. Jun uses horizontal washers. Write the volume as V = kπ. What is k?

   13568/15
4. 4.

   Kira spins the region between y = 1 and y = sin x, 0 ≤ x ≤ π/2, about the x-axis. To the nearest hundredth, what is k in V = kπ?

   0.79
5. 5.

   Luz spins the region between y = 2 and y = cos x, 0 ≤ x ≤ π/2, about the x-axis. To the nearest hundredth, what is k in V = kπ?

   5.5
6. 6.

   Noah spins the region between y = 2 and y = 1 + cos x, 0 ≤ x ≤ π, about the x-axis. To the nearest hundredth, what is k in V = kπ?

   7.85
7. 7.

   The region between y = R and y = 1, for 0 ≤ x ≤ 4, spins about the x-axis. Its volume is 32π. Pia solves for R > 1. What is R?

   3
8. 8.

   The region between y = R and y = 2, for 0 ≤ x ≤ 2, spins about the x-axis. Its volume is 24π. Ren solves for R > 2. What is R?

   4
9. 9.

   The region between y = R and y = 3, for 0 ≤ x ≤ 1, spins about the x-axis. Its volume is 16π. Tala solves for R > 3. What is R?

   5
10. 10.

    The region between y = R and y = 2, for 0 ≤ x ≤ 2, spins about the x-axis. Its volume is 64π. Zee solves for R > 2. What is R?

    6