Volumes by washers

Answer Key - Grade 12 Math Worksheet

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

1. 1.

   The region between y = x² and y = 4 spins about the line y = −1. Ari uses washers. Write the volume as V = kπ. What is k?

   1088/15
2. 2.

   The region between y = x² and y = 4 spins about the line y = −2. Bo uses washers. Write the volume as V = kπ. What is k?

   1408/15
3. 3.

   The region between y = x² and y = 1 spins about the line y = −1. Esme uses washers. Write the volume as V = kπ. What is k?

   64/15
4. 4.

   The region between y = x² and y = 9 spins about the line y = −1. Jun uses washers. Write the volume as V = kπ. What is k?

   2304/5
5. 5.

   The region between y = 5x and y = x² spins about the y-axis. Kira uses horizontal washers in y. Write the volume as V = kπ. What is k?

   625/6
6. 6.

   The region between y = 6x and y = x² spins about the y-axis. Luz uses horizontal washers in y. Write the volume as V = kπ. What is k?

   216
7. 7.

   The region between y = 7x and y = x² spins about the y-axis. Milo uses horizontal washers in y. Write the volume as V = kπ. What is k?

   2401/6
8. 8.

   The region between y = 8x and y = x² spins about the y-axis. Noah uses horizontal washers in y. Write the volume as V = kπ. What is k?

   2048/3
9. 9.

   The region between y = x + 6 and y = x² spins about the x-axis. Ren sets up washers. Which integral gives the volume?

   • π ∫ from −2 to 3 of (x + 6 − x²) dx
   • π ∫ from −2 to 3 of (x + 6 − x²)² dx
   • π ∫ from −2 to 3 of ((x + 6)² − x⁴) dx
   • π ∫ from −2 to 3 of (x⁴ − (x + 6)²) dx
10. 10.

    The region between y = √x and y = x/3 spins about the x-axis. Tala sets up washers. Which integral gives the volume?

    • π ∫ from 0 to 9 of (x − x²/9) dx
    • π ∫ from 0 to 9 of (x²/9 − x) dx
    • π ∫ from 0 to 9 of (√x − x/3)² dx
    • π ∫ from 0 to 9 of (√x − x/3) dx