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

CAL2.67 Shell Method Around a Coordinate Axis Worksheet

Download our free printable Calculus II Math worksheet on CAL2.67 Shell Method Around a Coordinate Axis. Ideal for classroom practice, homeschool learning, independent homework, and standardized test preparation. Available in both print-ready PDF and editable DOCX formats.

Choose your preferred download format:

100% Free • No registration or login required • Instant file access

Download PDF Download DOCX

Prefer interactive practice with instant grading and explanations?Practice Shell Method Around a Coordinate Axis Online

Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.67 Shell Method Around a Coordinate Axis. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.67 Shell Method Around a Coordinate Axis - Choose the correct shell-method radius, height, and volume integral. 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 CAL2.67 Shell Method Around a Coordinate Axis skill assessments:

Problem 1Difficulty: Mastery

The lower-side region R is bounded by x = 1 - y², x = 0, y = -1, and y = 0. R is revolved about the x-axis. Which shell-method setup is correct?

Ar = y, h = 1 - y², V = 2π∫_-1⁰ (y)(1 - y²) dy

Br = -y, h = 1 - y², V = π∫_-1⁰ (1 - y²)² dy

Cr = -y, h = y² - 1, V = 2π∫_-1⁰ (-y)(y² - 1) dy

Dr = -y, h = 1 - y², V = 2π∫_-1⁰ (-y)(1 - y²) dy

Solution & Explanation:Use horizontal shells: radius is the distance to the x-axis, so r = -y, and height is the length across the region, h = 1 - y². Thus V = 2π∫_-1⁰ (-y)(1 - y²) dy. Since y is negative on the interval, the distance to the x-axis is -y. A reversed height gives a negative slice length, and the π integral shown in a distractor is washer-style, not a shell setup.

Problem 2Difficulty: Mastery

The left-side region R is bounded by y = 1 - x², y = 0, x = -1, and x = 0. R is revolved about the y-axis. Which shell-method setup is correct?

Ar = x, h = 1 - x², V = 2π∫_-1⁰ (x)(1 - x²) dx

Br = -x, h = 1 - x², V = π∫_-1⁰ (1 - x²)² dx

Cr = -x, h = 1 - x², V = 2π∫_-1⁰ (-x)(1 - x²) dx

Dr = -x, h = x² - 1, V = 2π∫_-1⁰ (-x)(x² - 1) dx

Solution & Explanation:Use vertical shells: radius is the distance to the y-axis, so r = -x, and height is the length across the region, h = 1 - x². Thus V = 2π∫_-1⁰ (-x)(1 - x²) dx. Since x is negative on the interval, the distance to the y-axis is -x. A reversed height gives a negative slice length, and the π integral shown in a distractor is washer-style, not a shell setup.

Problem 3Difficulty: Mastery

The first-quadrant region R is bounded by y = x² and y = 2x. R is revolved about the x-axis. Which horizontal-shell setup is correct?

Ar = sqrt(y) - y/2, h = y, V = 2π∫_0⁴ (sqrt(y) - y/2)(y) dy

Br = y, h = sqrt(y) - y/2, V = 2π∫_0⁴ (y)(sqrt(y) - y/2) dy

Cr = y, h = sqrt(y) - y/2, V = π∫_0⁴ (sqrt(y) - y/2)² dy

Dr = y, h = y/2 - sqrt(y), V = 2π∫_0⁴ (y)(y/2 - sqrt(y)) dy

Solution & Explanation:Use horizontal shells: radius is the distance to the x-axis, so r = y, and height is the length across the region, h = sqrt(y) - y/2. Thus V = 2π∫_0⁴ (y)(sqrt(y) - y/2) dy. For horizontal shells, rewrite the boundaries as x = sqrt(y) and x = y/2. A reversed height gives a negative slice length, and the π integral shown in a distractor is washer-style, not a shell setup.

Want more practice questions with step-by-step guidance?

Practice All Questions Online

Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this CAL2.67 Shell Method Around a Coordinate Axis worksheet?

Click either the "Download PDF" or "Download DOCX" button at the top of the page. You can print the PDF directly from your browser or edit the DOCX file in Microsoft Word or Google Docs to tailor the questions to your students.

QIs this CAL2.67 Shell Method Around a Coordinate Axis worksheet free for teachers and homeschoolers?

Yes! All learning materials, worksheets, and practice resources on Free K12 Practice are 100% free for teachers, students, parents, tutors, and homeschooling families for non-commercial educational use. No account or subscription is required.

QCan students practice CAL2.67 Shell Method Around a Coordinate Axis online with instant feedback?

Yes! In addition to this printable worksheet, students can practice CAL2.67 Shell Method Around a Coordinate Axis interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

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 shell-method radius, height, and volume integral. 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).