Grade 12 · Math · Calculus

12th grade Volumes by disks worksheet

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Volumes by disks

Grade 12 Math Worksheet - Challenge Me

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

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?
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?
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?
Luz spins the region under y = eˣ, 0 ≤ x ≤ ln 3, about the x-axis. Write the volume as V = kπ. What is k?
Milo spins the region under y = eˣ, 0 ≤ x ≤ ln 5, about the x-axis. Write the volume as V = kπ. What is k?
Noah spins the region under y = eˣ, 0 ≤ x ≤ ln 6, about the x-axis. Write the volume as V = kπ. What is k?
Pia 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.
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.
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.
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.

Volumes by disks. Every version has 10 questions, and the answer key prints on the second page.

Standard: none (beyond CCSS)

solid of revolution: The solid swept out when a region spins around a line.

disk: A thin coin-shaped slice of area πr².

radius: The distance from the spin line to the curve.

Used the radius instead of its square. A disk's area is πr².

Squared twice the radius. The curve's height is the radius itself.

Used y as the radius of a horizontal disk; the radius is the x-distance, √y here.

What is the most common mistake with volumes by disks?

Used the radius instead of its square. A disk's area is πr².

Are these 12th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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