Volumes by washers
Grade 12 Math Worksheet
Circle the best answer, or write your answer on the line.
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?
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?
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?
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?
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?
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?
The region between y = x and y = x³, x ≥ 0 spins about the x-axis. Pia sets up washers. Which integral gives the volume?
- π ∫ from 0 to 1 of (x − x³) dx
- π ∫ from 0 to 1 of (x⁶ − x²) dx
- π ∫ from 0 to 1 of (x − x³)² dx
- π ∫ from 0 to 1 of (x² − x⁶) dx
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 (x⁴ − (x + 6)²) dx
- π ∫ from −2 to 3 of (x + 6 − x²)² dx
- π ∫ from −2 to 3 of ((x + 6)² − x⁴) dx
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 − x/3) dx
- π ∫ from 0 to 9 of (√x − x/3)² dx
- π ∫ from 0 to 9 of (x − x²/9) dx
- π ∫ from 0 to 9 of (x²/9 − x) dx
The region between y = 9 and y = x² spins about the x-axis. Zee sets up washers. Which integral gives the volume?
- π ∫ from −3 to 3 of (81 − x⁴) dx
- π ∫ from −3 to 3 of (9 − x²) dx
- π ∫ from −3 to 3 of (9 − x²)² dx
- π ∫ from −3 to 3 of (x⁴ − 81) dx