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

CAL2.74 Hydrostatic Force Worksheet

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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 (Select the correct pressure, depth, and area relationship in a fluid-force setup. 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 CAL2.74 Hydrostatic Force. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

CAL2.74 Hydrostatic Force - Select the correct pressure, depth, and area relationship in a fluid-force setup. 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 CAL2.74 Hydrostatic Force skill assessments:

Problem 1Difficulty: Mastery

A vertical plate is bounded by x = -ln(y) and x = ln(y) for 1 <= y <= e. The water surface is y = e + 1. Which integral gives the hydrostatic force?

AF = ∫_1^e γy[2 ln(y)] dy

BF = ∫_1^e γ(e + 1 - y)[2 ln(y)] dy

CF = ∫_1^e γ(e + 1 - y)(1/y) dy

DF = ∫_1^e γ(e + 1 - y)[ln(y)] dy

Solution & Explanation:At height y, the horizontal width is ln(y) - [-ln(y)] = 2 ln(y). The water surface is y = e + 1, so the depth is e + 1 - y, not y or the derivative 1/y.

Problem 2Difficulty: Mastery

A liquid has weight density γ. A vertical plate has top at depth a and bottom at depth b, and its width at depth h is proportional to h-a: w(h)=k(h-a). Which force integral is correct?

AF = ∫_a^b γ h k(h - a) dh

BF = ∫_a^b γ(h - a)kh dh with h replaced by h-a for pressure

CF = ∫_0^b γh k(h - a) dh

DF = ∫_a^b γ(b - h)k(h - a) dh

Solution & Explanation:The pressure uses actual depth h below the surface, while the width uses distance below the top, h-a. Mixing those two distances is a common setup error.

Problem 3Difficulty: Mastery

A vertical plate is 5 ft wide at the top, 11 ft wide at the bottom, and 6 ft tall. Its top is 4 ft below the surface. Let y measure distance down from the top. Which setup is correct?

AF = ∫_0⁶ 62.4y(5 + y) dy

BF = ∫_4¹⁰ 62.4y(5 + y) dy

CF = ∫_0⁶ 62.4(4 + y)(11 - y) dy

DF = ∫_0⁶ 62.4(4 + y)(5 + y) dy

Solution & Explanation:Depth is 4+y. Width increases from 5 to 11 over 6 ft, so w(y)=5+y. Bounds are 0 to 6 because y is measured from the top edge.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this CAL2.74 Hydrostatic Force 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 CAL2.74 Hydrostatic Force 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 CAL2.74 Hydrostatic Force online with instant feedback?

Yes! In addition to this printable worksheet, students can practice CAL2.74 Hydrostatic Force 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 (Select the correct pressure, depth, and area relationship in a fluid-force setup. 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.).