Volumes by washers

Answer Key - Grade 12 Math Worksheet - Building Confidence

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

1. 1.

   The region between y = 2x and y = x² spins about the x-axis. Ari uses washers. Write the volume as V = kπ. What is k?

   64/15
2. 2.

   The region between y = 3x and y = x² spins about the x-axis. Bo uses washers. Write the volume as V = kπ. What is k?

   162/5
3. 3.

   The region between y = x and y = x² spins about the x-axis. Esme uses washers. Write the volume as V = kπ. What is k?

   2/15
4. 4.

   The region between y = 4x and y = x² spins about the x-axis. Jun uses washers. Write the volume as V = kπ. What is k?

   2048/15
5. 5.

   The region between y = 3 and y = 1, 0 ≤ x ≤ 2, spins about the x-axis into a tube. Kira finds k in V = kπ. What is k?

   16
6. 6.

   The region between y = 5 and y = 2, 0 ≤ x ≤ 3, spins about the x-axis into a tube. Luz finds k in V = kπ. What is k?

   63
7. 7.

   The region between y = 4 and y = 2, 0 ≤ x ≤ 5, spins about the x-axis into a tube. Milo finds k in V = kπ. What is k?

   60
8. 8.

   The region between y = √x and y = x/2, for 0 ≤ x ≤ 4, spins about the x-axis. Pia names the washer's radii. Which is right?

   • R = √x, r = 0
   • R = √x, r = x/2
   • R = (√x) − (x/2), r = 0
   • R = x/2, r = √x
9. 9.

   The region between y = 5x and y = x², for 0 ≤ x ≤ 5, spins about the x-axis. Ren names the washer's radii. Which is right?

   • R = x², r = 5x
   • R = 5x, r = 0
   • R = 5x, r = x²
   • R = (5x) − (x²), r = 0
10. 10.

    The region between y = 4 − x² and y = 3, for −1 ≤ x ≤ 1, spins about the x-axis. Zee names the washer's radii. Which is right?

    • R = 4 − x², r = 0
    • R = 3, r = 4 − x²
    • R = 4 − x², r = 3
    • R = (4 − x²) − (3), r = 0