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

CAL2.71 Surface Area of Revolution Worksheet

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Q: Can students practice CAL2.71 Surface Area of Revolution online with instant feedback?

Yes! In addition to this printable worksheet, students can practice CAL2.71 Surface Area of Revolution interactively on our platform with automated grading, instant score tracking, and detailed step-by-step solutions.

Q: What 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 surface-area integral, radius, and arc-length component for a generated surface. 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).

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Calculus II Math worksheet provides structured practice on CAL2.71 Surface Area of Revolution. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.71 Surface Area of Revolution - Choose the correct surface-area integral, radius, and arc-length component for a generated surface. 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 CAL2.71 Surface Area of Revolution skill assessments:

Problem 1Difficulty: Mastery

A smooth curve C is rotated about a fixed axis in its plane. Which statement gives the most general surface-area setup used in this skill?

AS = π∫_C r² ds, where r is the distance to the axis.

BS = 2π∫_C y dx for every axis of rotation.

CS = 2π∫_C ds/r, where r is the slope of the curve.

DS = 2π∫_C r ds, where r is the nonnegative distance from the curve to the axis of rotation.

Solution & Explanation:The unifying formula is circumference times arc length: dS = 2πr ds. The radius r must be a nonnegative distance to the chosen axis; formulas using πr² are volume formulas, not surface-area formulas.

Problem 2Difficulty: Mastery

The curve y = 1 + cos x for 0 <= x <= π is rotated about the line y = 1. Which expression correctly handles the radius?

A2π∫_0^π cos x√(1+sin² x) dx

B2π∫_0^π (1+cos x)√(1+sin² x) dx

C2π[∫_0^(π/2) cos x√(1+sin² x) dx + ∫_(π/2)^π (-cos x)√(1+sin² x) dx]

Dπ∫_0^π cos² x dx

Solution & Explanation:The distance from y = 1+cos x to y = 1 is ∣cos x∣, which changes sign at π/2. The split integral is equivalent to 2π∫_0^π ∣cos x∣√(1+sin² x)dx.

Problem 3Difficulty: Mastery

The curve y = x³/6 + 1/(2x) for 1 <= x <= 2 is rotated about the x-axis. Which surface-area integral uses the correct radius and simplified ds?

A2π∫_1² x((x²+1/x²)/2) dx

B2π∫_1² (x³/6+1/(2x))((x²+1/x²)/2) dx

C2π∫_1² (x³/6+1/(2x))((x²-1/x²)/2) dx

Dπ∫_1² (x³/6+1/(2x))² dx

Solution & Explanation:The radius is y = x³/6 + 1/(2x). Since y' = x²/2 - 1/(2x²), the expression √(1+(y')²) simplifies to (x²+1/x²)/2 on this interval.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this CAL2.71 Surface Area of Revolution 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 CAL2.71 Surface Area of Revolution 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 CAL2.71 Surface Area of Revolution online with instant feedback?

Yes! In addition to this printable worksheet, students can practice CAL2.71 Surface Area of Revolution 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 surface-area integral, radius, and arc-length component for a generated surface. 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).