Free Printable WorksheetMathCalculus IIMath CurriculumAP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55

CAL2.65 Disk Method Around a Coordinate Axis Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.65 Disk Method Around a Coordinate Axis. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.65 Disk Method Around a Coordinate Axis - Choose the correct disk-method setup and computed volume for a solid of revolution. Standards: AP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Calculus II

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related CAL2.65 Disk Method Around a Coordinate Axis skill assessments:

Problem 1Difficulty: Mastery

The region bounded by x = 2 + sqrt(y), the y-axis, y = 1, and y = 4 is revolved about the y-axis. The coordinate units are centimeters. Which disk-method setup and computed volume are correct?

AV = pi∫_{1}⁴ (2 + sqrt(y)) dy = 32pi/3 cm³

BV = ∫_{1}⁴ (2 + sqrt(y))² dy = 229/6 cm³

CV = pi∫_{1}⁴ (2(2 + sqrt(y)))² dy = 458pi/3 cm³

DV = pi∫_{1}⁴ (2 + sqrt(y))² dy = 229pi/6 cm³

Solution & Explanation:Disks perpendicular to the y-axis use the distance from the curve to the y-axis as the radius, so the squared-radius term is (2 + sqrt(y))². Therefore V = pi∫_{1}⁴ (2 + sqrt(y))² dy = 229pi/6 cm³. The common error is to integrate the radius itself, omit pi, or double the radius as if the diameter were the radius.

Problem 2Difficulty: Mastery

The region bounded by y = 1 + sqrt(x), the x-axis, x = 1, and x = 4 is revolved about the x-axis. The coordinate units are centimeters. Which disk-method setup and computed volume are correct?

AV = pi∫_{1}⁴ (1 + sqrt(x)) dx = 23pi/3 cm³

BV = ∫_{1}⁴ (1 + sqrt(x))² dx = 119/6 cm³

CV = pi∫_{1}⁴ (1 + sqrt(x))² dx = 119pi/6 cm³

DV = pi∫_{1}⁴ (2(1 + sqrt(x)))² dx = 238pi/3 cm³

Solution & Explanation:Disks perpendicular to the x-axis use the distance from the curve to the x-axis as the radius, so the squared-radius term is (1 + sqrt(x))². Therefore V = pi∫_{1}⁴ (1 + sqrt(x))² dx = 119pi/6 cm³. The common error is to integrate the radius itself, omit pi, or double the radius as if the diameter were the radius.

Problem 3Difficulty: Mastery

The region bounded by x = 2/(y + 1), the y-axis, y = 0, and y = 3 is revolved about the y-axis. Which disk-method setup and computed volume are correct?

AV = pi∫_{0}³ (2/(y + 1)) dy = 4pi ln(2)

BV = pi∫_{0}³ (2/(y + 1))² dy = 3pi

CV = ∫_{0}³ (2/(y + 1))² dy = 3

DV = pi∫_{0}³ (2(2/(y + 1)))² dy = 12pi

Solution & Explanation:Disks perpendicular to the y-axis use the distance from the curve to the y-axis as the radius, so the squared-radius term is (2/(y + 1))². Therefore V = pi∫_{0}³ (2/(y + 1))² dy = 3pi. The common error is to integrate the radius itself, omit pi, or double the radius as if the diameter were the radius.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Calculus II Math students. It aligns with educational standard AP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55 (Choose the correct disk-method setup and computed volume for a solid of revolution. Standards: AP Calculus BC Unit 8; FL MA.912.C.5.5-C.5.7; CCSS.HSM; CCSS.HSN.Q.1-3; CCSS.MP2, MP4, MP6, MP7; Integrated Calculus II Standards CAL2-APP; TEKS 19 TAC section 111.55.).